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
[tex]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[/tex]
Thus the sequence is increasing by 2 raised to power 0, 1, 2 and so on
Thus the next three terms are found by:
[tex]33 + 2^5 =33 + 32= 65\\\\65 + 2^6 = 65 + 64 = 129\\\\129 + 2^7 = 129 + 128 = 257[/tex]
Thus the next three terms of sequence are 65, 129 and 257
