Question

What is the sum of the geometric sequence 3,15,75... if there are 7 terms ?

Answer 1

58593

Explanation:

The sum to n terms of a geometric sequence is

`S_(n)` =
`(a(r^n-1))/(r-1)`

where a is the first term and r the common ratio

r = 15 ÷ 3 = 75 ÷ 15 = 5 and a = 3, hence

`S_(7)` =
`(3(5^7-1))/(5-1)`

=
`(3(78125-1))/(4)` =
`(3(78124))/(4)` = 58593