What is the nth term of the geometric sequence 4, 8, 16, 32, ... ?

Solution:

A sequence in which the ratio between two consecutive terms is the same is called a geometric sequence.

The geometric sequence given is 4, 8, 16, 32, ...

Here a₁ = 4

a_n = nth term

r = 8/4 = 2

The formula is a_n = a.r^{n - 1}

Where a is the first term

n is the number of terms

r is the common ratio

Substituting the values

a_n = 4(2)^{n - 1}

Therefore, the nth term is a_n = 4(2)^{n - 1}.

What is the nth term of the geometric sequence 4, 8, 16, 32, ... ?

Summary:

The nth term of the geometric sequence 4, 8, 16, 32, ... is a_n = 4(2)^{n - 1}.