Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth.
-$$a _ { 2 } = - 16 , a _ { 5 } = 128$$
A) $\mathrm { a } _ { 1 } = 8 , \mathrm { r } = - 2$
B) $\mathrm { a } _ { 1 } = 8 , \mathrm { r } = - 0.5$
C) a $\mathrm { a } _ { 1 } = 128 , \mathrm { r } = - 0.5$
D) $\mathrm { a } _ { 1 } = 16 , \mathrm { r } = 2$

Question

Quizplus · Accepted Answer

Given $a_2 = -16$ and $a_5 = 128$, we can use the formula for the nth term of a geometric sequence, $a_n = a_1 \cdot r^{(n-1)}$, to find $a_1$ and $r$. From $a_2 = a_1 \cdot r^{(2-1)} = -16$ and $a_5 = a_1 \cdot r^{(5-1)} = 128$, we can solve for $a_1$ and $r$. Dividing $a_5$ by $a_2$, we get $r^3 = -8$, so $r = -2$. Substituting $r = -2$ into $a_2 = a_1 \cdot r$, we find $a_1 = 8$.

Find the First Term and the Common Ratio for the Geometric