Find an equation for the nth term of the sequence. -3, -12, -48, -192, …

Solution:

Given, the sequence is -3, -12, -48, -192,.......

First term, a = -3

Common ratio, r = -12/-3 = 4

This implies the series is in geometric progression.

The n-th term of the geometric sequence is given by

\(a_{n}=ar^{(n-1)}\)

Here, a = -3, r = 4

So, \(a_{n}=-3(4)^{(n-1)}\)

\(\\a_{n}=-3(4^{n}÷4^{1})\\a_{n}=\frac{-3}{4}(4^{n})\)

Therefore, the nth term of the sequence is \(a_{n}=\frac{-3}{4}(4^{n})\).

Find an equation for the nth term of the sequence. -3, -12, -48, -192, …

Summary:

An equation for the nth term of the sequence -3, -12, -48, -192,.... is \(\\a_{n}=-3(4^{n}-4^{-1})\\a_{n}=\frac{-3}{4}(4^{n})\).