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

1 Answer
sente
Dec 18, 2015

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

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