What is the sum of the geometric sequence 1, –6, 36, … if there are 6 terms?

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Answer 1 · 2016-01-25T17:17:41

The geometric sequence is #1,-6,36,....#

#a_2/a_1=(-6)/1=-6#

#a_3/a_2=36/-6=-6#

#implies# common ratio#=r=-6# and #a_1=1#

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 furst term, #r# is the common ratio.

Here #a_1=1#, #n=6# and #r=-6#

#implies Sum=(1(1-(-6)^6))/(1-(-6))=(1-46656)/(1+6)=(-46655)/7=-6665#

Hence, the sum is #-6665#