Find the geometric means in the sequence 4,_,_,_,324

Ayanna Goodman

Ayanna Goodman

Answered question

2022-11-14

Find the geometric means in the sequence 4,_,_,_,324

Answer & Explanation

Marshall Flowers

Marshall Flowers

Beginner2022-11-15Added 20 answers

It appears that questioner wants to know three middle terms in the geometric sequence {4,...,...,...,324}
Let the first term be a and common ratio be r.
Then five terms are { a , a r , a r 2 , a r 3 , a r 4 }
Hence a=4 and a r 4 = 324 , Dividing latter by former, we get
r 4 = 324 4 = 81 and hence r = ± 3
Hence geometric sequence is {4,12,36,108,324} or {4,−12,36,−108,324}
and middle terms are {12,36,108} or {−12,36,−108}

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