# What should be the next number in the series 1 , 8 , 243 , 256 , ?

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What should be the next number in the series 1 , 8 , 243 , 256 , ?
posted Sep 4, 2015

1^0 2^3 3^5 2^8 1^11

1 8 243 256 1

1 raised to n
2 raised to 3
3 raised to 5
4 raised to 4 or 2 raised to 8
5 raised to 3 sounds ok = 125

1 is for forming sequence 1 2 3 4 .... 5
8 for indicating sum of number and its power

After this 6 raised to 2. 36
7 raised to 1. 7
8 raised to 0. = 1

answer Sep 4, 2015 by anonymous
2 raised to 3 it is not 8.because 2+3=5 not 8.

2 and 3 do not add up to 8, so 2 raised to 3 does not fit in your pattern.

i.e.
1=1^2
8=2^3
243=3^5
256=4^4
the bases are counting numbers 1,2,3,....
the exponent also follows the increasing order but is never even if the base is not even.
so the next must be 5^7= 78125.

i.e
1^4=1
2^3=8
3^5=243
4^4=256
5^6=15625
power of this series are 4,3,5,4,6.
relation in power is -1 and +2.
4-1=3
3+2=5
5-1=4
4+2=6

78125

1^1
2^3
3^5
4^4
5^7

i.e. N^x; N is set of real positive integers
x is set of prime numbers if N is a prime
else x=N

answer Sep 18, 2015 by anonymous

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