Question

The 8th term of a GP is -7/32 find its common ratio if its first term is 28

Answer 1

Common ratio = -1/2

Explanation:

`\text{8}^(th)` term of a Geometric progression is given as
`(-7)/(32)`. The first term is given as
`28`.

Any general Geometric progression can be represented using the series
`a,ar,ar^(2),ar^(3),ar^(4)...\text{ }ar^(n-1)`.

The first term in such a GP is given by
`a`, common ratio by
`r`, and the
`n^(th)` term is given by
`ar^(n-1)`.

In the given GP,
`a=28;t_(8)=ar^(7)=(-7)/(32)\\\\28r^(7)=(-7)/(32)\\\\r^(7)=(-1)/(128)\\\\r=(-1)/(2)`

∴ Common ratio is
`(-1)/(2)`.