Find the sum of a finite geometric sequence from n = 1 to n = 6, using the expression −2(5)^n − 1? 1,223 −1,023 7,812 −7,812

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Answer 1 · 2018-07-26T05:33:02

#-7,812#

Sum #= sum_(n=1)^6 -2(5)^(n-1)#

Apply linearity.

Sum #= -2 * sum_(n=1)^6 5^(n-1)#

The sum is a geometric series with first term #a_1 = 5^0 =1# and common ratio #r =5#

We know that the sum of the first #n# terms of a geometric series is given by:

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

Hence, in this example:

Sum #= -2* (1(1-5^6))/(1-5)#

#= 1/2(1-15625)#

#= -15624/2 = -7,812#