Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth.
-$$a _ { 2 } = 4.5 , a _ { 7 } = 34.17$$
A) $\mathrm { a } _ { 1 } = 3 , \mathrm { r } = 0.67$
B) $\mathrm { a } _ { 1 } = 34.17 , \mathrm { r } = 0.67$
C) $\mathrm { a } _ { 1 } = 4.5 , \mathrm { r } = 1.5$
D) $a _ { 1 } = 3 , r = 1.5$

Question

Quizplus · Accepted Answer

The formula for the nth term of a geometric sequence is $ a_n = a_1 \cdot r^{n-1} $. Using the given terms $ a_2 = 4.5 $ and $ a_7 = 34.17 $, we can set up the equations: $ a_1 \cdot r = 4.5 $ and $ a_1 \cdot r^6 = 34.17 $. Solving these equations simultaneously gives $ a_1 = 3 $ and $ r = 1.5 $.

Find the First Term and the Common Ratio for the Geometric