Question

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

Answer 1

\[{\rm S}=\frac{a_1(1-r^n)}{1-r}\]

Answer 2

answer choices
1223
-1023
-7812
7812

Answer 3

can you identify the common ratio ?

Answer 4

5

Answer 5

yes

Answer 6

now, to find \(a_1\) plug in 1 for n

Answer 7

1223

Answer 8

what is the first term ?

Answer 9

-10

Answer 10

-2(5)^(n-1) => -2(5)^(1-1) => -2(5)^0 => -2(1) => -2

Answer 11

\[{\rm S_n}=\frac{a_1(1-r^{\ \rm n})}{1-r}=\frac{(-2)(1-5^6)}{1-5}\]

Answer 12

-3125

Answer 13

-7812