Find the indicated partial sum for the given geometric sequence.
-$\mathrm { s } _ { 6 } , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \frac { 1 } { 16 } , \ldots$
A) $\frac { 1 } { 64 }$

B) $\frac { 127 } { 128 }$

C) $\frac { 63 } { 64 }$

D) $\frac { 31 } { 384 }$

Question

Find the indicated partial sum for the given geometric sequence.
-$\mathrm { s } _ { 6 } , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \frac { 1 } { 16 } , \ldots$
A) $\frac { 1 } { 64 }$

B) $\frac { 127 } { 128 }$

C) $\frac { 63 } { 64 }$

D) $\frac { 31 } { 384 }$

Quizplus · Accepted Answer

The formula for the sum of a finite geometric sequence is 
$$S_n = \frac{a(1-r^n)}{1-r},$$
where $a$ is the first term, $r$ is the common ratio and $n$ is the number of terms.

In this case, we have $a = \mathrm{s}_1 = 1$, $r = \frac12$ and $n = 6$, so the sum of the first six terms is 
$$S_6 = \frac{1(1-1/2^6)}{1-1/2} = \frac{63}{64}.$$

Therefore, the answer is (C).

Find the Indicated Partial Sum for the Given Geometric Sequence s6,12,14,18,116,…\mathrm { s } _ { 6 } , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \frac { 1 } { 16 } , \ldotss6​,21​,41​,81​,161​,…

Find the Indicated Partial Sum for the Given Geometric Sequence $\mathrm { s } _ { 6 } , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \frac { 1 } { 16 } , \ldots$