Question

The second and fifth term of a geometric series are 750 and -6 respectively. Find the common ratio of and the first term of the series?

Answer 1

`r=-1/5,a_1=-3750`

Explanation:

The `color(blue)"nth term of a geometric sequence"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(a_n=ar^(n-1))color(white)(2/2)|)))`
where a is the first term and r, the common ratio.

`rArr"second term "=ar^1=750to(1)`

`rArr"fifth term "=ar^4=-6to(2)`

To find r, divide ( 2) by ( 1)

`rArr(cancel(a)r^4)/(cancel(a)r)=(-6)/750`

`rArrr^3=-1/125rArrr=-1/5`

Substitute this value into ( 1) to find a

`rArraxx-1/5=750`

`rArra=750/(-1/5)=-3750`