Find the 7th term of the geometric sequence where a1 = –2 and a5 = –512

Bayobusalue

Bayobusalue

Answered question

2022-11-02

Find the 7th term of the geometric sequence where a1 = –2 and a5 = –512

Answer & Explanation

erlentzed

erlentzed

Beginner2022-11-03Added 22 answers

First recognise that −512 is a power of −2; specifically - 512 = ( - 2 ) 9
As this is the fifth term, the power is 2 5 - 1 = 9
The nth term is therefore ( - 2 ) 2 n - 1
The 7th term will be ( - 2 ) 2 7 - 1 = ( - 2 ) 13 = 8192

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