Find the sum.
-$$\sum _ { k = 1 } ^ { n } 5 \cdot 7 ^ { k - 1 }$$

Name: Find the sum. -\[\sum _ { k = 1 } ^ { n } 5 \cdot 7 ^ { k - 1 }\]
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Question

Quizplus · Accepted Answer

This sum is a geometric series with the first term $a = 5$ (when $k=1$, $7^{k-1} = 7^0 = 1$), common ratio $r = 7$, and $n$ terms. The sum of a geometric series is given by $S_n = a\frac{1-r^n}{1-r}$. Substituting $a = 5$, $r = 7$, and simplifying gives $S_n = 5\frac{1-7^n}{1-7} = \frac{5}{6}(1-7^n)$, which matches option C.

Find the Sum ∑k=1n5⋅7k−1\sum _ { k = 1 } ^ { n } 5 \cdot 7 ^ { k - 1 }k=1∑n​5⋅7k−1

Find the Sum $\sum _ { k = 1 } ^ { n } 5 \cdot 7 ^ { k - 1 }$