Find $a _ { 1 }$ and and r for a geometric sequence { $\left\{ a _ { n } \right\}$ } from the given information.
-$a _ { 2 } = 18$ and $a _ { 7 } = 4,374$
A) $a _ { 1 } = 18$ and $r = 3$
B) $a _ { 1 } = 6$ and $r = 3$
C) $a _ { 1 } = 6$ and $r = 12$
D) $a _ { 1 } = 18$ and $r = 12$

Question

Quizplus · Accepted Answer

Given $a_2 = 18$ and $a_7 = 4,374$, 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 $r$. For $a_2$, $18 = a_1 \cdot r^{(2-1)}$, which simplifies to $18 = a_1 \cdot r$. For $a_7$, $4,374 = a_1 \cdot r^{(7-1)}$, which simplifies to $4,374 = a_1 \cdot r^6$. Solving these equations simultaneously, we find $a_1 = 6$ and $r = 3$.

Find a1a _ { 1 }a1​ And and R for a Geometric Sequence

Find $a _ { 1 }$ And and R for a Geometric Sequence