Find the 7th term of the geometric sequence where a1 = –4 and a5 = –1,024

Paloma Sanford

Paloma Sanford

Answered question

2022-10-25

Find the 7th term of the geometric sequence where a1 = –4 and a5 = –1,024

Answer & Explanation

veirenca77

veirenca77

Beginner2022-10-26Added 9 answers

The common ratio r of this geometric sequence is a 4th root of - 1024 - 4 = 256 = 4 4 , since a 5 = r 4 a 1
The possible Real 4th roots are ± 4
In either case:
a 7 = r 2 a 5 = 16 ( - 1024 ) = - 16384
So why do I say that a 7 may be 16384?
The Complex numbers ± 4 i are also 4th roots of 256.
If r = ± 4 i then r 2 = - 16 and we find:
a 7 = r 2 a 5 = ( - 16 ) ( - 1024 ) = 16384

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