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:

$S_{n}=\frac{a_{1}(1-r^{n})}{1-2}$

Using the known values:
$S_{8}=\frac{6(1-0.5^{8})}{1-0.5}$
$S_{8}=\frac{6(1-0.00390625)}{0.5}$
$S_{8}=\frac{6(0.99609375)}{0.5}$
$S_{8}=\frac{5.9765625}{0.5}$
$S_{8}=11.953125$