write the following in sigma notation $a^k+a^{2k} +a^{4k} +a^{8k} +a^{{16}k} ...+a^{{256}k}$

Question

I see the pattern being $2k$ on the power, and I thought the formula would just be $a^{(2k)}$, but i feel like im missing something else here ? Why is it not The summation from $a=1$ to $128 = a^{2k}$

Answer 1

Assuming you fix your fourth term:

$$\sum\limits_{n=0}^8 a^{2^n k}$$