Find the sum of the finite geometric sequence.? $$\sum _ { n = 1 } ^ { 7 } 2 ^ { n - 1 }$$ ?
A)43
B)22
C)127
D)63
E)31

Question

Quizplus · Accepted Answer

The problem provides the common ratio '2' and the first term '5'. It remains to find the number of terms. We can use the formula for the sum of a finite geometric sequence, which is  S_n = a(1-r^n) / (1-r), where n is the number of terms, a is the first term, and r is the common ratio. Plugging in the given values, we get S_n = 5(1-2^n) / (-1) for n terms. We notice that the numerator is equal to 5(2^n - 1), which means that S_n is divisible by 5 for all positive n. The only answer choice that is divisible by 5 is C, 127, so that is our answer.

Find the Sum of the Finite Geometric Sequence ∑n=172n−1\sum _ { n = 1 } ^ { 7 } 2 ^ { n - 1 }n=1∑7​2n−1

Find the Sum of the Finite Geometric Sequence $\sum _ { n = 1 } ^ { 7 } 2 ^ { n - 1 }$