Find these missing terms [__,8,__,128,....]

Jared Lowe

Jared Lowe

Answered question

2022-11-20

Find these missing terms [__,8,__,128,....]

Answer & Explanation

Milton Gilmore

Milton Gilmore

Beginner2022-11-21Added 20 answers

If the general term of the sequence is a n ( n = 1 , 2 , 3 , ... ) then we can rephrase the problem like this:
A geometric sequence has a 2 = 8 and a 4 = 128 . What are a 1 and a 3 ?
The general term of a geometric sequence is described by the formula:
a n = a r n - 1
where a is the initial term and r is the common ratio.
In our example, we find:
r 2 = a r 3 a r = a 4 a 2 = 128 8 = 16 = 4 2
So r = ± 4
If r=4 then:
a 1 = a 2 r = 8 4 = 2 and a 3 = a 2 r = 8 4 = 32
If r=−4 then:
a 1 = a 2 r = 8 - 4 = - 2 and a 3 = a 2 r = 8 ( - 4 ) = - 32

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