Question

2,3,5,9,17,33 what are the next three terms?

Answer 1

The next three terms of sequence are 65, 129 and 257

Solution:

Given sequence is:

2, 3, 5, 9, 17, 33

We have to find the next three terms in sequence

Let us find the logic used in this sequence

$2 + 2^0 = 2 + 1 = 3\\\\3 + 2^1 = 3 + 2 = 5\\\\5 + 2^2 = 5 + 4 = 9\\\\9 + 2^3 = 9 + 8 = 17\\\\17 + 2^4 = 17 + 16 = 33$

Thus the sequence is increasing by 2 raised to power 0, 1, 2 and so on

Thus the next three terms are found by:

$33 + 2^5 =33 + 32= 65\\\\65 + 2^6 = 65 + 64 = 129\\\\129 + 2^7 = 129 + 128 = 257$

Thus the next three terms of sequence are 65, 129 and 257