Find the sum of a finite geometric sequence from n = 1 to n = 6, using the expression -2(5)n - 1.

Sum of finite geometric sequence is - 216 .

Step-by-step explanation:

Given : expression -2(5)n - 1.

To find : Find the sum of a finite geometric sequence from n = 1 to n = 6.

Solution : We have given expression

-2 (5) n - 1.

For n = 1

-2(5) 1 -1

-10 -1 =  - 11.

For n = 2

-2(5) 2 -1

-20 -1 = -21.

For n = 3

-2(5) 3 -1.

-30 -1

-31.

For n = 4

-2(5) 4 -1

-40 - 1

-41.

For n = 5

-2(5) 5 -1.

-50 -1

-51.

For n = 6

-2(5) 6 -1

-60 - 1

-61 .

Sum of finite geometric sequence : -11 + (-21)  + (-31) + (-41) + (-51) + (-61) .

-11 -21 -31 -41 -51 - 61 .

= -216.

Therefore, Sum of finite geometric sequence is - 216 .

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step-by-step explanation:

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