Question

How do you find the nth term rule for 1, 4, 16, 64?

Answer 1

In the given question you were asked to find the nth term rule for 1, 4, 16, 64. This problem can be solved with the help of Geometric Progression. You should use the formula of the nth term of GP to solve this problem. So let us see how we can solve this problem.

Complete Step by Step Solution:
In the given problem we have to find the nth term rule for 1, 4, 16, 64. This problem can be solved with the nth term formula of GP. In this problem, we have the first term, a = 1, and the common ratio, r = 4.
For finding the nth term of GP we will use $a{r^{n - 1}}$ formula.

So the nth term of GP for this problem = ${1.4^{n - 1}}$
$= {4^{n - 1}}$

Note:
In the above solution, we used the formula of the nth term of GP that is $a{r^{n - 1}}$, where a is the first term and r is the common ratio. A geometric progression is an order in which every term is determined by multiplying or dividing the preceding term with a fixed number known as the common ratio. The GP of a is $ar,a{r^2},a{r^3}......a{r^n}$.