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

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

Mathematics
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\[{\rm S}=\frac{a_1(1-r^n)}{1-r}\]
answer choices 1223 -1023 -7812 7812
can you identify the common ratio ?

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Other answers:

5
yes
now, to find \(a_1\) plug in 1 for n
1223
what is the first term ?
-10
-2(5)^(n-1) => -2(5)^(1-1) => -2(5)^0 => -2(1) => -2
\[{\rm S_n}=\frac{a_1(1-r^{\ \rm n})}{1-r}=\frac{(-2)(1-5^6)}{1-5}\]
-3125
-7812

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