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

1 Answer
Dec 18, 2015

Answer:

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#