Find the next three terms in the geometric sequence -16, 4, , , ...

Clara Dennis

Clara Dennis

Answered question

2022-11-21

Find the next three terms in the geometric sequence -16, 4, , , ...

Answer & Explanation

Teagan Raymond

Teagan Raymond

Beginner2022-11-22Added 14 answers

Since it is a geometric sequence ( x n ) , there is a constant ratio r = ( x n + 1 x n ) = 4 - 16 = - 1 4
So if a=−16 is the first term x 1 , then general term is given by x n = a r n - 1 = - 16 ( - 1 4 ) n - 1
Hence the 3rd term, x 3 = - 16 ( - 1 4 ) 3 - 1 = - 1
Similarly x 4 = 1 4 and x 5 = - 1 16

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