Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth.
-$$a _ { 2 } = 224 , a _ { 7 } = 7$$
A) $\mathrm { a } _ { 1 } = 14 , \mathrm { r } = 2$
B) $a _ { 1 } = 896 , r = 0.5$
C) $\mathrm { a } 1 = 448 , \mathrm { r } = 0.5$
D) $a _ { 1 } = 7 , r = 2$

Question

Quizplus · Accepted Answer

The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$. Using $a_2 = 224$ and $a_7 = 7$, we can solve for $r$ and $a_1$. Solving gives $r = 0.5$ and $a_1 = 448$.

Find the First Term and the Common Ratio for the Geometric