How do you find #S_n# for the geometric series #a_1=1#, #a_6=-243#, r=-3?

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Answer 1 · 2017-09-02T12:59:51

#-182#

firstly we need to write out the GP

#S_n=1+(-3)+(9)+(-27)+(81)+(-243)#

multiply the series by the common ratio #r=-3#

#-3S_n=" "color(red)((-3)+(9)+(-27)+(81)+(-243))+(729)#

#S_n" "=1+color(red)((-3)+(9)+(-27)+(81)+(-243))#

Subtract the two. It will be noticed that the terms in red will cancel.

#-4S_n=729-1#

#S_N=728/-4=-182#