How to Calculate the nth Term of a Geometric Sequence: Formula and Examples

Explicit Formula for Geometric Sequence

The explicit or general formula for a geometric sequence is given by:

an = a1 * r^(n-1)

where:
an represents the nth term of the sequence,
a1 is the first term of the sequence,
r is the common ratio between consecutive terms of the sequence,
n is the position of the term in the sequence

The explicit or general formula for a geometric sequence is given by:

an = a1 * r^(n-1)

where:
an represents the nth term of the sequence,
a1 is the first term of the sequence,
r is the common ratio between consecutive terms of the sequence,
n is the position of the term in the sequence.

To use this formula, you need to know the values of a1 and r. The first term, a1, is the starting number of the sequence, while the common ratio, r, is the factor by which each term is multiplied to obtain the next term.

For example, if you are given a geometric sequence with a first term of 2 and a common ratio of 3, and you want to find the 5th term of the sequence, you would plug in the values into the formula:

a5 = 2 * 3^(5-1)
= 2 * 3^4
= 2 * 81
= 162

Therefore, the 5th term of this sequence is 162.

Note: It is important to remember that the position of the term, n, starts from 1. So, if you want to find the first term, you should substitute n = 1 in the formula.

More Answers: