How do you find S_n for the geometric series a_1=4, r=0.5, n=8?

2 Answers
Dec 6, 2016

S_n = 7.96875

Explanation:

there are two equations to find S_n of a geometric series.
if r is greater than 1, we use S_n=a*(r^n -1)/(r-1)
and if r is less than 1, we use S_n=a*(1-r^n)/(1-n)

in this question r is less than 1. so we use the second equation to find S_n

S_n = 4* (1-0.5^8)/(1-0.5)

therefore S_n = 7.96875

Dec 6, 2016

S_8 = color(green)(7.96875)

Explanation:

Given an initial value color(red)(a_1), and a geometric increment of color(blue)n
the color(brown)n^(th) term is given by the formula:
color(white)("XXX")S_color(brown)n=color(red)(a_1)((1-color(blue)r^color(brown)n)/(1-color(blue)r))

Using the given values (and a calculator)
color(white)("XXX")S_8 = 7.96875