What is the next number of the following sequence 36, 117, 166, 335, 360, 441, ..........

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11 Jul 2016 Sequence

What is the next number of the following sequence
36, 117, 166, 335, 360, 441, ..........

OPtion

1) 522
2) 581
3) 542
4) 576
5) 457
6) 442
7) 466
8) 505
9) 445
10)None of these

Solution

36
36 + (3+6)^2 = 36+9^2 = 36+81 = 117 [Number+(Sum of digit)^2]
117 + 7^2 = 117+49 = 166 [Number+(last digit)^2]
166 + (1+6+6)^2 = 166+13^2 = 166+169 = 335 [Number+(Sum of digit)^2]
335 + 5^2 = 335+25 = 360 [Number+last digit)^2]
360 + (3+6+0)^2 = 360+9^2 = 360+81 = 441 [Number+(Sum of digit)^2]
Similarly
441 + 1^2 = 441+1 = 442 [Number+last digit)^2]

Option 6)

Correct Option: 6 Best Solution (20)

bhaskar   8 years AGO

36+(9*9)
117+(7*7)
166+(13*13)
335+(5*5)
360+(9*9)
441+(1*1)

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ABHINAV PUSHPAM   8 years AGO

36+(3+6)^2=36+81=117
117+7^2=166
166+(6+6+1)^2=335
335+5^2=360
360+(4+4+1)^2=360+81=441
441+1^2=442
Option 6)

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MRITUNJAY   8 years AGO

36+(3+6)^2=36+81=117
117+7^2=166
166+(6+6+1)^2=335
335+5^2=360
360+(4+4+1)^2=360+81=441
441+1^2=442
option 6

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Mukund Manohar   8 years AGO

Starting from 36,the square of the sum of digits and the square of the last digit is added to the number alternately.
36 = 36 + (3+6)^2 = 36 + 81 = 117
117 = 117 + 7^2 = 117 + 49 = 166
166 = 166 + (1+6+6)^2 = 166 + 169 = 335
335 = 335 + 5^2 = 335 + 25 = 360
360 = 360 + (3+6+0)^2 = 360 + 81 = 441
441 = 441 + 1^2 = 441 + 1 = 442

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RAHUL KUMAR   8 years AGO

36+(3+6)^2=36+81=117
117+7^2=166
166+(6+6+1)^2=335
335+5^2=360
360+(4+4+1)^2=360+81=441
441+1^2=442

option 6

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Anchal jain   8 years AGO

36 117 166 335 360 441....442
81 49 169 25 81......1
square of
9 7 13 5 9.......-1
-2 +6 -8 +4 ... -10
441 + (-1)^2=442

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Ankit Kumar   8 years AGO

36
36+square of((0+3)+6)=117
117+ square of(7)=166
166+ square of(7+6)=335
335+ square of(5)=360
360+ square of((3+6)+0)=441
so
441+ square of(1)=442

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Avdhesh Singh Rana   8 years AGO

difference b/w numbers are 81,49,169,25,81
3+6=9^2=81
36+81=117
last digit of 117=7^2=49
117+49=166
sum of digits of 1+6+6=13^2=169
166+169=335
similar way last number 441 then its last digit is 1=1^2=1
441+1=442

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Siva   8 years AGO

36
117=36+(3+6)^2
166=117+7^2
335=166+(1+6+6)^2
360=335+5^2
441=360+(3+6+0)^2
442=441+1^2.

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madanpal vishwakarma    8 years AGO

given series

36,117,166,335,360,441...

we relate the term as describe below..

36,(6+3)^2 +36=117,(7)^2+117=166,(1+6+6)^2+166=335,(5)^2+335=360,(3+6+0)^2+360=441

so next term is (1)^2+441=442

So option 6 is correct

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RISHABH   8 years AGO

36=3+6=9^2=81
117=7^2=49
And, so on taking alternately taking the first no. and sum up all the digits of a number and squaring it & adding the no. obtained to get the second number.Secondly taking the last digit and squaring it and adding to the no. to get the next no.
So, in 441 taking the last digit i.e 1 and squaring it and adding it to 441 to get the next no. as (441+1)=442

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Akshat Sood   8 years AGO

117=(3+6)^2+36
166=(1+7-1)^2+117
335=(6+6+1)^2+166
.
.
442=(1+4-4)^2+441

OPTION(6)

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Shreeprasad Bhat   8 years AGO

The differences between yhe numbers are perfect squares.
Also there is alternative odd and even numbers.
To find the number to be squared
1) For even, add the digits and square and it to the number in the sequence to get next number in the sequence.
2) For odd, square the last digit and add it to the number in the sequence to get the next number in the sequence

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Lakshmipathi   8 years AGO

36>>3+6=9==>9^2=81; 36+81=117
117>>last digit square 7^2 +117=166
''''''''
441+1^2==442

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Jaikumar Bhatia   8 years AGO

36=>36+(3+6)^2=117
117=>117+(7)^2=166
166=>166+(1+6+6)^2=335
335=>335+(5)^2=360
360=>360+(3+6+0)^2=441
441=>441+(1)^2=442
Number+(add digits) ^2..(i)
Number+(last digit) ^2....(ii)
(i) and (ii) alternatively
Ans is 442
Option is (6)

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Anup Sahay   8 years AGO

the numbers at odd place add the square of sum of digits of their digits to themselves to get the next number on even place
, while numbers on even place add the square of last digit to them to get the the next number on next odd place, i.e.
36: is at 1st position i.e. at odd place
so,
(3+6)*(3+6)=9*9=81
36+81=117
117: is at 2nd position i.e at even position ,
so,
117+(7*7)=117+49=166
similarly series goes so
441+(1*1)=441+1=442
since 441 is on even position
and we get next number on odd position as 442

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Nishtha shree   8 years AGO

the difference between 36 and 117 is 81 which is square of (3+6) similarly 117 and 166 is 49 which square of the last digit 7 again from 166 and 335 the difference is 169 square of(1+6+6)=13 in this fashion square of last digit of 441 that is 1^2 will be added to 441 so result will be 441+1=442

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T.uma maheswari   8 years AGO

36(3+6=9) so 36+(9*9)=117.
117,(1+1+7=9)....so 117+(7*7)=166
166,(1+6+6)=13 so 166(13*13)=335
335,(3+3+5)=11 so 335(5*5)=360
360,(3+6+0)=9 so 360+(9*9)=441
441,(4+4+1)=9 so 441+(1*1)=442 alternatively once we have to square it and once with last digit

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N.Sowjanya   8 years AGO

36+9^2=117
166+13^2=335
335+9^2=441
117+7^2 silillarly 441+162=442

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RAVAL   8 years AGO

even digit is a (odd no.s digit summation)^2
odd digit is (even no.s unit digit's square)
e.g
36 = 9^2 = 81 = 81 + 36 = 117
117 = 7^2 = 49 = 49 + 117 = 166
same....
441 = 1^2 = 1 = 1+441 = 442

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