Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth.
-$$a _ { 2 } = 20.8 , a _ { 9 } = 130.52$$
A) $\mathrm { a } _ { 1 } = 20.8 , \mathrm { r } = 1.3$
B) $\mathrm { a } _ { 1 } = 16 , \mathrm { r } = 0.77$
C) $\mathrm { a } _ { 1 } = 130.52 , \mathrm { r } = 0.77$
D) $a _ { 1 } = 16 , r = 1.3$

Question

Quizplus · Accepted Answer

The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{(n-1)}$. Given $a_2 = 20.8$ and $a_9 = 130.52$, we can set up two equations: $20.8 = a_1 \cdot r^{(2-1)}$ and $130.52 = a_1 \cdot r^{(9-1)}$. Solving these equations simultaneously, we find $a_1 = 16$ and $r = 1.3$.

Find the First Term and the Common Ratio for the Geometric