How to find the nth term of a geometric sequence

Nth term of a geometric sequence

The nth term of a geometric sequence is given by the formula

$a_n = a_1r^n$

$a_1 =$ first term
$r=$ common ratio
$a_n =$ nth term
Find the nth term

1. Find the 10^th term of the sequence 5, -10, 20, -40, ….
Answer
-2560

2. Find the 15th term of the sequence $\displaystyle{\frac{1}{2}}, 1, 2, 4,$ …
Answer
$2^{13}$
Find the indicated term in the geometric sequence

1. $a_1=9,r=\displaystyle{\frac{1}{2}}, a_9=$
Answer
$\displaystyle{\frac{9}{256}}$

2. $a_1=5, r=3, a_5=$

Answer
405
Find the first three terms in the sequence given the general formula

1. $a_n=4\cdot 2^n$
Answer
8, 16, 32

2. $a_n=3\cdot\left(\displaystyle{-\frac{1}{3}}\right)^{n-1}$
Answer
$3, -1, \displaystyle{\frac{1}{3}}$
Find a formula for the general term of the following sequence

6, 12, 24, 48, …

Answer
$a_n=6\cdot 2^{n-1}$