Find the indicated term of a geometric sequence from the given information.
-$a _ { 5 } = \frac { 81 } { 16 }$ and $r = - \frac { 3 } { 4 }$. Find $a _ { 1 }$.
A) 16
B) $- 12$
C) $- \frac { 64 } { 3 }$
D) $- 16$

Question

Quizplus · Accepted Answer

The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{(n-1)}$. Given $a_5 = \frac{81}{16}$ and $r = -\frac{3}{4}$, we can substitute these values into the formula to find $a_1$. So, $a_5 = a_1 \cdot (-\frac{3}{4})^{(5-1)}$, which simplifies to $\frac{81}{16} = a_1 \cdot (-\frac{3}{4})^4$. Since $(- \frac{3}{4})^4 = \frac{81}{256}$, we can solve for $a_1$ by multiplying both sides by the reciprocal of $\frac{81}{256}$, which gives $a_1 = 16$.

Find the Indicated Term of a Geometric Sequence from the Given