What is the next number of the following sequence 81, 0, 21, 44, 69,.....

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17 Nov 2014 Sequence What is the next number of the following sequence 81, 0, 21, 44, 69,.....: OPtion
1) 25
2) 89
3) 24
4) 96
5) 64
6) 72
7) 61
8) 76
9) 88
10)None of these; Correct Option: 4 Best Solution (99)

CHANDAN KUMAR 10 years AGO

0+21=21
21+23=44
44+25=69
69+27=96

Like? Yes (5) | No

Chandra chur anand 10 years AGO

9^2%100=81
10^2%100=0
11^2%100=21
.......
14^2%100=96 is the ans...

Like? Yes (9) | No (4)

Alok singh 10 years AGO

81+19=100-100=0 if result is equal or more than 100
0+21=21
21+23=44
44+25=69
69+27=96

Like? Yes (3) | No

Anubhav jain 10 years AGO

21 INC . 23 25 27
ANS 96

Like? Yes (2) | No

NEHA KUMARI 10 years AGO

0+21=21
21+23=44
44+25=69
69+27=96

Like? Yes (2) | No

Akshay 10 years AGO

9*9=081
10*10=100
11*11=121
12*12=144
13*13=169
14*14=196
Remove the most significant bot from all the right hand side number.
hence 96.

Like? Yes (6) | No (5)

priyanka 10 years AGO

21*1=21
22*2=44
23*3=69
24*4=96...................

Like? Yes (1) | No

kumar 10 years AGO

81-0=81
81-21=60
81-44=37
81-69=12
now,

diff of 81-60 =21
diff of 60-37=23 and
diff of 37-12=25
So,
12-x=27
therefore, x=-15
so,
81-(-15)=96
is the next number

Like? Yes (1) | No

ranjithreddy 10 years AGO

Removing the digit in 100s place
9*9=81.........81
10*10=100......0
11*11=121.........21
12**12=144........44
and so on....
14*14=196......96 is the answer

Like? Yes (2) | No (1)

prem kumar chaudhary 10 years AGO

9*9=81
10*10=100
11*11=121
12*12=144
13*13=169
14*14=196
ans=96

Like? Yes (3) | No (2)

P Niranjan 10 years AGO

19*9 = 171 =1+7 1 = 81

20*0 = 0
21*1 = 1
22*2 = 44
23*3 = 69
24*4 = 96

Like? Yes (2) | No (1)

Bhanoj 10 years AGO

These are the last two digits of the squares of the numbers starting from 9
9*9=081 last two digits 81
10*10=100 last two digits 00
11*11=121 last two digits 21
12*12=144 last two digits 44
13*13=169 last two digits 69
14*14=196 last two digits 96
so 96 is the one which coming next in the series.

Like? Yes (2) | No (1)

nayan jain 10 years AGO

becoz after 0 , series is increment in order to add 21,23,25....... to the previous no.

Like? Yes (1) | No

Anshul Shrivastava 10 years AGO

81+(19+0)=100=00
100+(19+2)=121=21
121+(19+4)=144=44
144+(19+6)=169=69
169+(19+8)=196=96

Like? Yes (2) | No (2)

vamsi priyanka 10 years AGO

the diff between the 21,44 is 23
and diff between the 44 ,69 is 25
nd diff between the 69,96 may be 27

Like? Yes (2) | No (2)

chanchal 10 years AGO

21*1=21, 22*2=44,23*3=69,24*4=96

Like? Yes (2) | No (2)

Sonam 10 years AGO

choose last two digits of square of a no.
9*9=81
10*10=100
11*11=121
12*12=144
13*13=169
14*14=196

81,0,21,44,69,96

Like? Yes (2) | No (2)

KRISHAN MURARI 10 years AGO

9^2=81
10^2=100~0 (last two number)
11^2=121~21 (last two number)
12^2=144~44 (last two number)
13^2=169~69 (last two number)
14^2=196~96 (last two number)

Like? Yes (1) | No (1)

Hemadri 10 years AGO

(9)2=81
(10)2=100
(11)2=121
(12)2=144
(13)2=169
(14)2=196

Like? Yes (1) | No (1)

LOKESH KUMAR 10 years AGO

21-0=21
44-21=23
69-44=25
96-69=27
So series of increasing order of 2

Like? Yes (1) | No (1)

sachin verma 10 years AGO

81=9^2
00=last two digits of(10^2)
21=last two digits of(11^2)
44=last two digits of(12^2)
69=last two digits of(13^2)
So, next is
last two digits of(14^2)=96

Like? Yes (1) | No (1)

Siddharth 10 years AGO

The series is made of the last two terms of squares of 9,10,11,12,13,14 respectively
so
81,0,21,44,69,96

Like? Yes (1) | No (1)

Harshal R Satapute 10 years AGO

guess

Like? Yes (1) | No (1)

Rohit Sharma 10 years AGO

Looking at the last 3 number and their combination this looks like to be the next number.

Like? Yes (1) | No (1)

Parag Wagh 10 years AGO

last 2 digits are there:
13^2=169 so 69
14^2=196 so 96
option 4) 96

Like? Yes (1) | No (1)

MINTU KUMAR GUPTA 10 years AGO

last two digit of square of 9,10,11,12,13,14,15.....
81 100 121 144 169 196
ans is 96

Like? Yes (1) | No (1)

Rahul Rathod 10 years AGO

9^2=81 mod 100=81
10^2=100 mod 100=0
11^2=121 mod 100=21
12^2=144 mod 100=44
13^2=169 mod 100=69
similarly
14^2=196 mod 100=96

Like? Yes (2) | No (3)

Kushagra Tiwari 10 years AGO

Here a(n) = n^2 reduced mod 100.
AS
9^2 = 081 => 81
write square of no and then take last two digits of its starting from 9
similarly
10^2 = 100 => 00
11^2 = 121 => 21
12^2 = 144 => 44
13^2 = 169 => 69

so the next term is
14^2 = 196 => 96

which is in option no 4

Like? Yes (6) | No (7)

Saranjit Singh 10 years AGO

taking last two digits of perfect squares starting frm 81.

Like? Yes (2) | No (3)

Udhaya kumar 10 years AGO

n^2 mod 100.....
where n = 9,10,11,12,13,14...respectively....
14^2 mod 100 = 96.......

Like? Yes (2) | No (3)

Rahul 10 years AGO

81 (-81) = 0,
0 (+21) = 21,
21 (+23) = 44,
44 (+25) = 69,
69 (+27) = 96

Like? Yes (2) | No (3)

priya saha 10 years AGO

taking last two digit of squares of no. greater than and equal to 9

9^2=81 81
10^2=100 0
11^2=121 21
12^2=144 44
13^2=169 69
14^2=196 96 (ansr)

Like? Yes (2) | No (3)

Anand Dwivedi 10 years AGO

96 Will be Correct Answer
.
a(n) = n^2 reduced mod 100.

Like? Yes (2) | No (3)

SUCHETA BISWAS 10 years AGO

14*14=196
ignore 1

Like? Yes (2) | No (3)

RAKESH 10 years AGO

9^2, 10^2, 11^2, 12^2, 13^2, 14^2

take last two digit of the series
14^2 --------------> 96

Like? Yes (1) | No (3)

Abhishek Vishwakarma 10 years AGO

Here a(n) = n^2 reduced mod 100.
AS
9^2 = 081 => 81

similarly
10^2 = 100 => 00
11^2 = 121 => 21
12^2 = 144 => 44
13^2 = 169 => 69

so the next term is
14^2 = 196 => 96

Like? Yes (1) | No (3)

Dr.Dipin Singh 10 years AGO

taking last two digits of 81,100,121,14,169 (13^2) and then 196(14^2).
hence 96 is next number.

Like? Yes (2) | No (4)

Surit Datta 10 years AGO

1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 21, 44, 69, 96, 25, 56
it is the series where after square of 10
the numbers are written as
11 square = 121 we write it as 21
12 square = 144 we write it as 44
13 square = 169 we write it as 69
14 square = 196 we write it as 96
That's it..

Like? Yes (1) | No (3)

Abhishek mani 10 years AGO

81+19=100(last two digit)=0
0+21=21
21+23=44
44+25=69
69+27=96so answer is (4)

Like? Yes (2) | No (4)

anuj gupta 10 years AGO

N^2 MOD 100.
9^2 MOD 100=81.
10^2 MOD 100=0.
11^2 MOD 100=21.
12^2 MOD 100=44.
13^2 MOD 100=69.
14^2 MOD 100=96.

SO ANS IS 96.

Like? Yes (1) | No (3)

lakshmi 10 years AGO

If an integer is congruent to 0 mod 10, then x^2 = 0^2 = 0 mod 10

i.e., if x = 0 mod 10 then the last digit of x^2 is 0.
a(n) = n^2 reduced mod 100.

Like? Yes (1) | No (3)

Sandeep Kumar 10 years AGO

81= 9*9;
0= 10*10;
21= 11*11;
44= 12*12;
69=13*13;
96=14*14;
so 96 will be the answer.

Like? Yes (1) | No (3)

purushothama 10 years AGO

If an integer is congruent to 0 mod 10, then x^2 = 0^2 = 0 mod 10

i.e., if x = 0 mod 10 then the last digit of x^2 is 0.
a(n) = n^2 reduced mod 100.

Like? Yes (1) | No (3)

jayalakshmi 10 years AGO

If an integer is congruent to 0 mod 10, then x^2 = 0^2 = 0 mod 10

i.e., if x = 0 mod 10 then the last digit of x^2 is 0.
a(n) = n^2 reduced mod 100.

Like? Yes (1) | No (3)

bhagya 10 years AGO

If an integer is congruent to 0 mod 10, then x^2 = 0^2 = 0 mod 10

i.e., if x = 0 mod 10 then the last digit of x^2 is 0.
a(n) = n^2 reduced mod 100.

Like? Yes (1) | No (3)

CHANDA VIJAYALAKSHMI 10 years AGO

If an integer is congruent to 0 mod 10, then x^2 = 0^2 = 0 mod 10

i.e., if x = 0 mod 10 then the last digit of x^2 is 0.
a(n) = n^2 reduced mod 100.

Like? Yes (1) | No (3)

NAVEEN KUMAR 10 years AGO

9*9=81.............81
10*10=100............00
11*11=121..............21
12*12=144............44
13*13=169.............69
14*14=196..............96 only consider unit & tenth place
hence,option (4) is correct

Like? Yes (1) | No (3)

MANISH KUMAR SINGH 10 years AGO

The pattern is square of a number mod by 100.
like 9^2%100=81
10^2%100=0
11^2%100=21
12^2%100=44
13^2%100=69
14^2^100=196

Like? Yes (1) | No (3)

Mani kandan 10 years AGO

ans is option 4)96

Periodic with period 50: (0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 21, 44, 69, 96, 25, 56, 89, 24, 61, 0, 41, 84, 29, 76, 25, 76, 29, 84, 41, 0, 61, 24, 89, 56, 25, 96, 69, 44, 21, 0, 81, 64, 49, 36, 25, 16, 9, 4, 1) and next term is 0. The period is symmetrical about the "midpoint" 25.
add the odd digit with the number and it reach 100, then take 100 as a zero.then continue add the odd digit with the number

Like? Yes (1) | No (3)

Supriya Mondal 10 years AGO

Here we took last 2 digit of a square number
9^2=081(here last two digit is 81)
10^2=100(here last two digit is 00)
11^2=121(here last two digit is 21)
12^2=144(here last two digit is 44)
13^2=169(here last two digit is 69)
14^2=196(here last two digit is 96)
So the answer is 96

Like? Yes (1) | No (3)

Tark Patel 10 years AGO

first number is 81 which is square of 9 so
starting from 9 onwards do the sqquare of numbers in sequence and divide by it with 100 then write the remainders,

9^2 = 81 / 100 = 81 (remainder)

10^2 = 100 / 100 = 0 (remainder)

11^2 = 121 / 100 = 21 (remainder)

12^2 = 144 / 100 = 44 (remainder)

13^2 = 169 / 100 = 69 (remainder)

answer is

14^2 = 196 / 100 = 96 (remainder)

Like? Yes (1) | No (3)

Sanu Panji 10 years AGO

answer is 96

coz:-

(9^2)mod100=81
(10^2)mod100=0
(11^2)mod100=21
(12^2)mod100=44
(13^2)mod100=69
(14^2)mod100=96

so correct is option (4)

Like? Yes (1) | No (3)

Anoop Tiwari 10 years AGO

9^2+0,0,1^2+20,2^2+40,3^2+60 so next term will be.......
4^2+80=96
hence option 4) is correct

Like? Yes (1) | No (3)

Mathan Raj 10 years AGO

Its adding 21, 23, 25 sequentially

Like? Yes (1) | No (3)

Narasapu Hari prasad 10 years AGO

Ans is 96 option 4
the series is like this
9*9,10*10,11*11,12*12,13*13,14*14
81,100,121,144,169,196
take last two digits of every number
81,0,21,44,69,96

Like? Yes (1) | No (3)

sandineni kiran 10 years AGO

if we neglect the first number, the series is increased with 21,23,25,27
69+27=96

Like? Yes (1) | No (3)

santosh kumar patel 10 years AGO

ans: 96

Like? Yes (2) | No (4)

satyam sharma 10 years AGO

9^2=081
10^2=100
11^2=121
12^2=144
13^2=169
14^2=196
last two digit of each number is the required series
so answer is 96
correct option is 4

Like? Yes (1) | No (3)

sayantani jana 10 years AGO

the diff between 0 and 21 is 21 ,21and 44 is 23 ,69 and 44 is 25so the difference b/w the differences is 2 i.e(23-21=2,25-23=2). so the next term will be [69+(25+2)]=(69+27)=96.

Like? Yes (1) | No (3)

sravani 10 years AGO

2*1*10 + 1*1=21

2*2*10 + 2*2=44
2*3*10 + 3*3=69
2*4*10 + 4*4=96

Like? Yes (1) | No (3)

balu 10 years AGO

0-21=21 diff,
21-44=23 diff,
44-69=25 diff,
69-96=27 diff...

Like? Yes (1) | No (3)

K.ARun 10 years AGO

9^2=81 -----> 81
10^2=100 ----->0
11^2=121 ----->21
12^2=144 ----->44
13^2=169 ----->69
14^2=196 ----->96

so.. 96 :) :)

Like? Yes (1) | No (3)

raviteja 10 years AGO

last two digits of no's are given in the series.so the next no is 14 square last two digits are 9&6 so answer is 96

Like? Yes (1) | No (3)

Shivan kumar jha 10 years AGO

9*9=81
10*10=100
11*11=121
12*12=144
13*13=169
14*14=196
take last 2 digit so
ans =96

Like? Yes (1) | No (3)

Nikita Kumari 10 years AGO

9*9=81
10*10=100
11*11=121
12*12=144
13*13=169
we have considered only 2 digits from left side
in the same way next number of the series will be: 96

since 14*14= 196
and 2 digits from left will be '96'.

Like? Yes (1) | No (3)

Jigyasa Kumar 10 years AGO

the difference between consecutive nos. from 0 is following order 21, 23, 25 so the next no. will be 96

Like? Yes (1) | No (3)

SUBHASH TULSYAN 10 years AGO

19*9=171=>(1+7)1=81
20*0=000=>(0+0)0= 0
21*1=021=>(0+2)1=21
22*2=044=>(0+4)4=44
23*3=069=>(0+6)9=69
24*4=096=>(0+9)6=96.........(Answer)

Like? Yes (1) | No (3)

~Sandeep~ 10 years AGO

Series is based on following formula : n^2 mod 100
n starts from 9

Like? Yes (2) | No (4)

kamal 10 years AGO

last digit of squares 1,4,9,16,25,36,49,64,81,0,21,44,69,96,25,56,.....and so on

Like? Yes (1) | No (3)

VIVEK KUMAR BARANWAL 10 years AGO

14*14=196
so answer is 96.

Like? Yes (1) | No (3)

Emanuel Abhishek Murmu 10 years AGO

21-0= 21
44-21= 23
69-44= 25

so, 69+27= 96
next term in series is 96.

Like? Yes (1) | No (3)

Rajat Jain 10 years AGO

21*1,22*2,23*3,24*4

Like? Yes (1) | No (3)

Mani Shankar 10 years AGO

9*9 = 81
10*10 = 100
11*11 = 121
12*12 = 144
13*13=169
14*14= 196
so ans is 96

Like? Yes (1) | No (3)

P.Nikhil Reddy 10 years AGO

By adding consecutive odd numbers from 19,21...

Like? Yes (1) | No (3)

Ashish Kumar chhabra 10 years AGO

Last Two Digits Of Squares of numbers But Except 10

Like? Yes (1) | No (3)

abhishek narayan 10 years AGO

14*14=196 neglecting 1st term so ans is 96

Like? Yes (1) | No (3)

bikash tiwari 10 years AGO

9*9=81
10*10=100
11*11=121
12*12=144
13*13=169
14*14=196
after crossing two digit no. ignore first digit of 3digit no
so and becomes 96 ,ignore 1

Like? Yes (2) | No (4)

sanjeev kumar 10 years AGO

ans 96

Like? Yes (1) | No (3)

abhishek agrawal 10 years AGO

0+21=21
21+23=44
44+25=69
69+27=96

Like? Yes (1) | No (3)

Pushkar lal dangi 10 years AGO

81+19=100
0+21=21
21+23=44
44+25=69
69+27=96

Like? Yes (1) | No (3)

Shreya Tiwari 10 years AGO

Here a(n) = n^2 reduced mod 100.
AS
9^2 = 081 => 81

similarly
10^2 = 100 => 00
11^2 = 121 => 21
12^2 = 144 => 44
13^2 = 169 => 69

so the next term is
14^2 = 196 => 96

Like? Yes (1) | No (4)

Md.Sultan Khichi 10 years AGO

9^2=81
10^2=100=00
11^2=121=21
12^2=144=44
13^2=169=69
14^2=196=96
Ans. 96

Like? Yes (1) | No (4)

dhanaseelan 10 years AGO

0+21=21
21+23=44
44+25=69
69+27=96
so option 4

Like? Yes (1) | No (4)

P.Pandeeswari 10 years AGO

the series will be
(0+0)%100=0
(0+1)%100=1
(1+3)%100=4
(4+5)%100=9
(9+7)%100=16 .........
(64+17)%100=81
(81+19)%100=0
(0+21)%100=21
(21+23)%100=44
(44+25)%100=69
(69+27)%100=96

so the ans is option 4)

Like? Yes (3) | No (6)

abhilasha 10 years AGO

the difference between consecutive nos. from 0 is following order 21, 23, 25 so the next no. will be 96

Like? Yes (1) | No (4)

Aparna Bhattacharya 10 years AGO

Periodic with period 50: (0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 21, 44, 69, 96, 25, 56, 89, 24, 61, 0, 41, 84, 29, 76, 25, 76, 29, 84, 41, 0, 61, 24, 89, 56, 25, 96, 69, 44, 21, 0, 81, 64, 49, 36, 25, 16, 9, 4, 1) and next term is 0.
Option: 4

Like? Yes (1) | No (4)

dara naga anjani prasad 10 years AGO

between 0 & 21, 21& 44, 44& 69 and the diff is 21 , 23, 25, next number 27 if we added 69+27=96.

Like? Yes (1) | No (4)

swaroopfrancis 10 years AGO

81,100,121,144,169,196...squares

Like? Yes (1) | No (4)

AMREEN 10 years AGO

9^2=81
10^2=100
but take only last two digits.
11^2=121 take,21
12^2=144 take 44
13^2=169 take only 69
now next is 14^2=196
then take only 96 answer

Like? Yes (1) | No (4)

Male priyanka 10 years AGO

21-0=21
44-21=23
69-44=25
96-69=27
In the answer the difference is only 2.

Like? Yes (1) | No (4)

Dipali Badade 10 years AGO

0+21=21
21+23=44
44+25=69
69+27=96

Like? Yes (1) | No (4)

Jitendra Prasad 10 years AGO

9^2=81
10^2=100
11^2=121
12^2=144
13^2=169
14^2=196
then
14^2=96
Then seen two digit in square of the no.
ans=96

Like? Yes (1) | No (4)

Deepak prajapati 10 years AGO

9*9=81
10*10=100=00
11*11=121=21
12*12=144=44
13*13=169=69
14*14=196=96

Like? Yes (2) | No (5)

Devendra Kumar 10 years AGO

As the last digit of the series is of square of the number so the ans is 96

Like? Yes (1) | No (4)

ARJUN PRASAD 10 years AGO

take only two digit 9^2=81,10^2=100 take only last two digit,13^2=169 ie69 and so on... so 14^2=196 ie 96

Like? Yes (2) | No (5)

Sanchit Kapoor 10 years AGO

Each consecutive number is the last two digits of the square of natural number starting from 9
9^2 =81
10^2=100=0
11^2=121=21
12^2=144=44
13^2=169=69
So 14^2=196=96
Hence option 4 is correct.

Like? Yes (3) | No (7)

BHASKAR MANDAL 10 years AGO

these are the remainder when a perfect square is divided by 100
9^2 = 81 = 100 *0 +81 , r = 81
10^2 = 100/100 = 1*100 +0 , r = 0
11^2 = 121 /100 = 1*100 +21 , r = 21
.......
14^2 = 196 /100 = 1*100 + 96 , r = 96
so option 4 is the correct answer.

Like? Yes (1) | No (5)

APPIKONDA SANTOSH NAIDU 10 years AGO

21-0=21
44-21=23
69-44=25
96-69=27
so ans is=96

Like? Yes (1) | No (5)

Santosh Kumar Behera 10 years AGO

9*9=81 last two digit 81
10*10=100 last two digit 00 so 0
11*11=121 last two digit 21
12*12=144 last two digit 44
13*13=169 last two digit 69
14*14=196 last two digit 96 so ans is 4

Like? Yes (1) | No (5)

Dimple

India

Punjab

Time: 00:01:33

Points

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What is the next number of the following sequence 81, 0, 21, 44, 69,.....

M4maths Previous Puzzles

17 Nov 2014 Sequence

What is the next number of the following sequence
81, 0, 21, 44, 69,.....

OPtion

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