Question

Find the missing term of the geometric sequence. 45 ___ 1620

Answer 1

A geometric sequence has a common ratio. Let that ratio be r. Then you get the sequence:

`45,45r,45r^(2)`
You know that the third term is 1620, so just solve for r:

`45r^(2)=1620 \\ r^(2)=36 \\ r=\pm6`
So the common ratio is either 6 or -6. That means there are two possible missing terms:

`45r \\ =45(\pm6) \\ =\pm270`