Question

What is the eighth term of the sequence 2,8,32,128

Answer 1

It's a geometric sequence.

$2,8,32,128,... \\ \\ a_1=2 \\ r=\frac{a_2}{a_1}=\frac{8}{2}=4 \\ \\ a_n=a_1 \times r^{n-1} \\ a_8=2 \times 4^{8-1} \\ a_8=2 \times 4^7 \\ a_8=2 \times 16384 \\ a_8=32768$

The eighth term of the sequence is 32768.