Question

What is a1 for the geometric sequence for which a8= -3584 and a3 = 112 ?

Answer 1

The first term is 28.

Explanation:

Given: 8th term of Geometric sequence ,
`a_8=-3584`

and 3rd term of Geometric Sequence,
`a_3=112`

We have to find First term of given geometric Sequence.

Let a be the first term of geometric sequence.

We know that,

`a_n=ar^(n-1)`

So,

`(a_8)/(a_3)=(ar^(8-1))/(ar^(3-1))=(-3584)/(112)`

`(r^(7))/(r^(2))=-32`

`r^5=-32`

`r=-2`

So,
`a_3=112`

`a*(-2)^(2)=112`

`a=(112)/(4)=28`

Therefore, The first term is 28.