Question

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

Answer 1

Answer:

The first term is 28.

Step-by-step 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,

$\frac{a_8}{a_3}=\frac{ar^{8-1}}{ar^{3-1}}=\frac{-3584}{112}$

$\frac{r^{7}}{r^{2}}=-32$

$r^5=-32$

$r=-2$

So, $a_3=112$

$a\times(-2)^{2}=112$

$a=\frac{112}{4}=28$

Therefore, The first term is 28.