Question

What is the sum of a 7–term geometric series if the first term is –6, the last term is –24,576, and the common ratio is 4?

Answer 1

`S_7 = -32 768`

Explanation:

The sum to n terms of a geometric series is found using:

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

where a is the first term and r , the common ratio.

here a = - 6 and r = 4

`rArr S_7 =( (-6)(4^7 - 1 ))/(4 - 1 ) = ((-6)(16 384 ))/3 = - 32 768`