What is the sum of the geometric sequence –3, 21, –147, … if there are 6 terms?

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Answer 1 · 2016-01-25T17:39:48

#a_2/a_1=21/-3=-7#

#a_3/a_2=-147/21=-7#

#implies# common ratio#=r=-7# and #a_1=-3#

Sum of geometric series is given by

#Sum=(a_1(1-r^n))/(1-r)#

Where #n# is number of terms, #a_1# is the first term, #r# is the common ratio.

Here #a_1=-3#, #n=6# and #r=-7#

#implies Sum=(-3(1-(-7)^6))/(1-(-7))=(-3(1-117649))/(1+7)=(-3(-117648))/8=352944/8=44118#

Hence, the sum is #44118#.