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How do you find #S_n# for the geometric series #a_1=80#, r=-1/2, n=7?

1 Answer

Soumalya Pramanik

Feb 2, 2018

#53.75#

Explanation:

Just use the formula for finding the sum of #n# terms while the common ratio.

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

Substituting the values,

#S_n = (80(1 - (-1/2)^7))/(1 - (-1/2)) = (80 * (1 + 1/128))/(1 + 1/2) = (80 * 129/128)/(3/2) = (80.625)/(1.5) = 53.75#

It makes sense that The sum is actually less than the first term of the Geometric Progression, As #r = -1/2 < 1#

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