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

1 Answer
Jul 26, 2018

-7,812

Explanation:

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