Find a formula for the n th term of the geometric sequence. Assume that n begins with 1. $a_{1}=10, a_{2}=2$
A) $a_{n}=10\left(\frac{1}{5}\right)^{n-1}$
B) $a_{n}=2^{n-1}$
C) $a_{n}=2(5)^{n-1}$
D) $a_{n}=2(5)^{n}$
E) $a_{n}=10\left(\frac{1}{5}\right)^{x}$

Question

Quizplus · Accepted Answer

Since it is a geometric sequence, we know that the ratio between consecutive terms is constant. Let's call this ratio "r". Thus, we have:
$$\frac{a_{2}}{a_{1}} = r \Rightarrow \frac{2}{10} = r \Rightarrow r = \frac{1}{5}$$
Now we can use this ratio to find the n-th term:
$$a_{n} = a_{1}r^{n-1} = 10\left(\frac{1}{5}\right)^{n-1}$$
Therefore, choice A is the correct answer.

Find a Formula for the N Th Term of the Geometric