M4maths Previous Puzzles

02 Jun 2014 Sequence

What is the next number of the following sequence
1, 4, 11, 24, 47, 88, 163, .....

OPtion

1) 263
2) 279
3) 301
4) 208
5) 199
6) 258
7) 304
8) 274
9) 317
10)None of these

Solution

Differences of elements are the sum of two series
02, 04, 08, 16, 32, 64
01, 03, 05, 07, 09, 11

03, 07, 13, 23, 41, 75 Sum of these two series

Option 7)

Correct Option: 7 Best Solution (18)

Saraswathy   11 years AGO

Take difference of differences...

1.....4.....11.....24.....47.....88.....163....(x)
...3.....7.....13......23.....41.....75....(y)
......4.....6......10.....18......34....(z)
.........2......4......8......16.....(a)

So a = 32
z = 34+32 = 66
y = 75+66 = 141
x = 163+141 = 304

Ans : 304 (Option 7)

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Varunraj Reddy   11 years AGO

1, 4, 11, 24, 47, 88, 163, .....

0^2+1=1
1^2+(1*2+1)=1+3=4
2^2+(3*2+1)=4+7=11
3^2+(7*2+1)=9+15=24
4^2+(15*2+1)=16+31=47
5^2+(31*2+1)=25+63=88
6^2+(63*2+1)=36+127=163
7^2+(127*2+1)=49+255=304

Answer is Option 7)

Like? Yes (5) | No (3)  

Udhaya kumar   11 years AGO

(x+2^n+y)
where x as previous number
n=1,2,3,4......
y=1,3,5,7,9.......
163+2^7+13 = 304.......

Like? Yes (4) | No (3)  

rajani   11 years AGO

By taking the differences of differences b/w no.s we have to add 141 to the last no.
1 4 11 24 47 88 163(+141) 304
3 7 13 23 41 75(+66) 141
4 6 10 18 34 (+32)66
2 4 8 16 32

Like? Yes (2) | No (1)  

pankaj kumar   11 years AGO

4-1= 3
11-4=7
24-11=13
47-24= 23
88-47= 41
163-88= 75

3 7 13 23 41 75
7= 3*2+1
13=7*2-1
23 =13*2-3
41= 23*2-5
75= 41*2-7
similarly next no. is 75*2-9 =141

so ans is 141+163 =304

Like? Yes (2) | No (1)  

Komala.G   11 years AGO

Option (7)
1 +2^1+1 =4
4 +2^2+3 =11
11 +2^3+5 =24
24 +2^4+7 =47
47 +2^5+9 =88
88 +2^6+11 =163
163 +2^7+13 = 304

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P.Someshwar Reddy   11 years AGO

Difference of the numbers
4-1=3
11-4=7
24-11=13
47-24=23
88-47=41
163-88=75

the difference of difference of the numbers are
7-3=4(2^1+2)
13-7=6(2^2+2)
23-13=10(2^3+2)
41-23=18(2^4+2)
75-41=34(2^5+2)

so next number in the above sequence is
2^6+2=66

adding this to the initial difference we get it as
66+75=141
Adding this to the sequence we get it as
163+141=304

So the next number in the sequence is 304 option 7

Like? Yes (1) | No (1)  

pawan kumar chhipa   11 years AGO

1,4,11,24,47,88,163,z
difference b/w
3,7,13,23,47,75,y
difference b/w difference
4,6,10,18,34,x
difference b/w difference
2,4,8,16,p and power of 2 so value
come at p is 32
at x is 32+34=66
at y is 66+75=141
and at z is 141+163=304 is ans.

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Sukanya   11 years AGO

1 4 11 24 47 88 163 304

3 7 13 23 41 75 141

4 6 10 18 34 66

2 4 8 16 32

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T.Aravinth kumar   11 years AGO

163+141=304

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Ngarumsang    11 years AGO

difference between each nos.
3,7,13,23,41,75,141,..
differences of difference nos.,
4,6,10,18,34,...
now,
sum of differences of difference no.-2 produces the next differences of difference no.
i.e,
4+4-2=6
6+6-2=10
10+10-2=18
and so on...
hence 34+34-2=66.
so, 66+75=141
and 141+163=304.

Like? Yes (1) | No (1)  

shree   11 years AGO

163+141=304

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raju kumar   11 years AGO

1*2,2^2,2^3,2^4..last 2^5
this u will get after some factorization(steps)
304

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indrajeet yadav   11 years AGO

1^2=1+(2*0)=1
2^2=4+(2*0)=4
2^3=8+(3*1)=11
2^4=16+(4*2)=24
2^5=32+(5*3)=47
.....................
similarly
2^8=256+(8*6)=304

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piyushpallaw   11 years AGO

let us consider
common difference=d , n=0
next term= previous term + (d+(2+2^n))

first term=1
1+(2+2^0)=4
4+(3+(2+2^1))=11
11+(7+(2+2^2))=24
24+(13+(2+2^3))=47
47+(23+(2+2^4))=88
88+(41+(2+2^5))=163
163+(75+(2+2^6))=304

Like? Yes (1) | No (1)  

susmit   11 years AGO

third order differences are 2,4,8,16...
next difference is 32
then finding second order differences and the first order difference will be 140
ans : 163+141=304

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snair   11 years AGO

The difference between the consecutive numbers are 3,7,13,23,41,75.
Taking difference of the above series: 4,6,10,18,34
Again the difference: 2,4,8,16
thats is 2^n.
hence going backwards we get the next number as (163+32+34+75) = 304

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SIBNATH HALDER   11 years AGO

option 7 ans

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