Question

A geometric progression has 99 terms, the first term is 12 and the last term is 48. What is the 50-th term?

Answer 1

21.5

Explanation:

geometric progression formula:
`A_(n)`=A*
`r^(n-1)`

where An is nth term

A is first term

r is common ratio

given
`A_(99)` = 48

A=12

we find r

48=12 *
`r^(99-1)`

48/12=
`r^(98)`

`\sqrt[98]{4}`=r

r=1.014

so to find 50th term

`A_(50)`=12*
`1.012^(50-1)`

`A_(50)`=21.53