Find the sum of the arithmetic sequence.
-$$\frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \frac { 3 } { 32 }$$
A) $\frac { 7 } { 32 }$
B) 93
C) $\frac { 93 } { 32 }$
D) $\frac { 1 } { 8 }$

Question

Quizplus · Accepted Answer

The given sequence is not an arithmetic sequence; it's a geometric sequence with the first term $a = \frac{3}{2}$ and the common ratio $r = \frac{1}{2}$. The sum of the first $n$ terms of a geometric sequence is given by $S_n = a \frac{1-r^n}{1-r}$ for $r \neq 1$. Here, $n = 5$, so $S_5 = \frac{3}{2} \frac{1-(\frac{1}{2})^5}{1-\frac{1}{2}} = \frac{3}{2} \frac{1-\frac{1}{32}}{\frac{1}{2}} = 3 \times \frac{31}{32} = \frac{93}{32}$.

Find the Sum of the Arithmetic Sequence 32,34,38,316,332\frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \frac { 3 } { 32 }23​,43​,83​,163​,323​

Find the Sum of the Arithmetic Sequence $\frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \frac { 3 } { 32 }$