How to find the nth term of a geometric sequence?

A geometric sequence can comprise any number of terms, and we can calculate the exact value of any term in that sequence.

Answer: nth term of the geometric progression can be found out using the formula a_n = ar^{n-1}

Go through the examples to understand the formula better.

Explanation:

A geometric sequence is a sequence where every term bears a constant ratio to its preceding term.

nth term of the sequence is given by: a_n = ar^{(n- 1)}

Let's find the 6^th term in the geometric sequence 3, 12, 48, ...

Here, a₁ = 3, r = 12/3 = 4  a₆ = 3 × 4^6-1 = 3072

Do you know how to calculate the nth term of the geometric progression if the first two terms are given as 10 and 20?

First, you need to calculate the common ratio r of the geometric series by dividing the second term by the first term.

So, r = 20 / 10 = 2   

Then, substitute the values of the first term a and the common ratio r into the formula of the nth term of the geometric progression.

a_n = a r^n-1 = 10(2)ⁿ⁻¹ = 10 × 2ⁿ / 2 = 5(2)ⁿ

Thus, the nth term of the geometric progression can be found out using the formula a_n = ar^n-1