Question

List the first five terms of each sequence, and identify them as arithmetic or geometric.

1. A(n + 1) = 1/4 times A(n) for n≥1 and A(1) = 8

Answer 1

8, 2, 1/2, 1/8, 1/32 - geometric sequence

Explanation:

`A_(n+1)=1/4A_(n) \\n\geq 1\\A_(1)=8\\A_(2)=1/4A_(1)=1/4*8=2\\A_(3)=1`/4A_(2)=1/4*2=1/2\\A_(4)=1`/4A_(3)=1/4*1/2=1/8\\A_(5)=1`/4A_(4)=1/4*1/8=1/32\\8, 2, 1/2, 1/8, 1/32 - geometric sequence \\q=1/4`