Question

The first term of a geometric sequence is 6, and the ratio (multiplier) is 0.5. What is the sum of the first 8 terms, rounded to the nearest tenth?

Answer 1

The sum of the first
`n` terms of a geometric sequence is given by:


`S_(n)=(a_(1)(1-r^(n)))/(1-2)`

Using the known values:

`S_(8)=(6(1-0.5^(8)))/(1-0.5)`

`S_(8)=(6(1-0.00390625))/(0.5)`

`S_(8)=(6(0.99609375))/(0.5)`

`S_(8)=(5.9765625)/(0.5)`

`S_(8)=11.953125`