Question

2,8, 32, 128 Arithmetic, Geometric, or neither? Explicit: _ Geometric Recursive:

Answer 1

Answer:

Geometric

Step-by-step explanation:

$\frac{8}{2} = 4 \\ \\ \frac{32}{8} = 4 \\ \\ \frac{128}{32} = 4$

Here, common ratio (r = 4) is same, therefore given sequence is a geometric progression.

Recursive formula is given as:

$t_n= ar^{n-1}\\\\\therefore t_n= 2\times 4^{n-1}\\\\\therefore t_n= 2\times 2 ^{2(n-1)}\\\\\therefore t_n= 2\times 2 ^{2n-2}\\\\\therefore t_n= 2 ^{2n-2+1}\\\\\therefore t_n= 2 ^{2n-1}$

Answer 2

the sequense between them are times4