Question

How do you find the 8th term in this geometric sequence 8, 4, 2, 1, ...?

Answer 1

Find the common ratio and use it to find that the eighth term is
`1/16`

Explanation:

Given a geometric series `(ar^n)` with initial term `a` and common ratio `r`, we may find `r` by dividing any term after the first by the prior term, as
`(ar^k)/(ar^(k-1)) = r`

Thus in the given sequence, dividing the second term by the first gives
`r = 4/8 = 1/2`

The `n^(th)` term in the sequence is `ar^(n-1)`. Thus, as the given sequence has an initial term `a = 8`, the eighth term is

`ar^7 = 8(1/2)^7 = 1/16`