Write the first 4 terms of the geometric sequence with $a _ { 1 } = \frac { 1 } { 5 }$ , $r 0$ , $6 ^ { \text {th } }$ term is $\frac { 32 } { 5 }$ .
A) $\frac { 1 } { 5 } , \frac { 2 } { 5 } , \frac { 4 } { 5 } , \frac { 8 } { 5 }$
B) $\frac { 1 } { 5 } , \frac { - 2 } { 5 } , \frac { 4 } { 5 } , \frac { - 8 } { 5 }$
C) $\frac { 1 } { 5 } , \frac { 2 } { 5 } , 2 , \frac { 4 } { 5 }$
D) $\frac { 1 } { 5 } , \frac { - 2 } { 5 } , 2 , \frac { - 4 } { 5 }$

Question

Write the first 4 terms of the geometric sequence with $a _ { 1 } = \frac { 1 } { 5 }$ , $r > 0$ , $6 ^ { \text {th } }$ term is $\frac { 32 } { 5 }$ .
A) $\frac { 1 } { 5 } , \frac { 2 } { 5 } , \frac { 4 } { 5 } , \frac { 8 } { 5 }$
B) $\frac { 1 } { 5 } , \frac { - 2 } { 5 } , \frac { 4 } { 5 } , \frac { - 8 } { 5 }$
C) $\frac { 1 } { 5 } , \frac { 2 } { 5 } , 2 , \frac { 4 } { 5 }$
D) $\frac { 1 } { 5 } , \frac { - 2 } { 5 } , 2 , \frac { - 4 } { 5 }$

Quizplus · Accepted Answer

Given $a_1 = \frac{1}{5}$ and $a_6 = \frac{32}{5}$, we can use the formula for the $n$th term of a geometric sequence, $a_n = a_1 \cdot r^{(n-1)}$, to find $r$. Plugging in the values for $a_6$ and $a_1$, we get $\frac{32}{5} = \frac{1}{5} \cdot r^{5}$, which simplifies to $r^5 = 32$. Solving for $r$, we find $r = 2$. Therefore, the first four terms are $\frac{1}{5}, \frac{2}{5}, \frac{4}{5}, \frac{8}{5}$, which matches option A.

Write the First 4 Terms of the Geometric Sequence With a _