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#