Question

Nn a G.P. there are 8 terms, sum of the first 4 terms is 45 and sum of last four terms is 720, find the first term and positive common ratio.​

Answer 1

Answer: The first term is 3 and the positive common ratio is 2.

Explanation:

Let the sum of the eight terms of the geometric series be (a+ar+a
`r^(2)` +a
`r^(3)` +a
`r^(4)`+a
`r^(5)`+a
`r^(6)`+a
`r^(7)`)

Given that a+ar+a
`r^(2)`+a
`r^(3)`=45

a
`r^(4)`+a
`r^(5)`+a
`r^(6)`+a
`r^(7)`=720

Now,

`r^(4)`(a+ar+a
`r^(2)`+a
`r^(3)`)=720

we already know the value of (a+ar+a
`r^(2)`+a
`r^(3)`) which is 45

=>
`r^(4)`=720/45= 16.

then, r= ±2

Since we want a positive common ratio, then, r=2.

Now, a+ar+a
`r^(2)`+a
`r^(3)`=45⇒ a=3.