Question

The first term of a geometric sequence is 3 and the fifth term is 768 what is the sum of the first 9 terms of the corresponding series

Answer 1

262143

Explanation:

`a_(n) = a r^(n - 1)` a = 3 n = 5
`a_(5) = 768`

768 = 3(r)^4 where r is the common ratio

r^4 = 256

r = 4

S =
`(a(r^(n)-1) )/(r - 1)` n = 9 r = 4 a = 3

S =
`(3(4^(9)-1) )/(4 - 1)` =
`(3(262144-1) )/(3)`

= 262143