What is the third term of a sequence that has the first term of 3 and a common ratio of 3?

Solution:

When the ratio between any two consecutive terms in a sequence is the same, it is called a geometric progression.

The general term of any geometric progression = a r^{n - 1}

Given that, a = 1^st term = 3, r = 3, n = Number of terms = 3

The nth term of geometric progression with common ratio r can be calculated using the formula a r^{n - 1}

⇒ n^th term = a r^{n - 1}

⇒ 3^rd term = 3 × 3^{(3 - 1)} = 3 × 3² = 27

You can use the online Geometric sequence calculator to calculate the terms.

Thus, the third term of a geometric progression with first term 3 and common ratio 3 is 27.

What is the third term of a sequence that has the first term of 3 and a common ratio of 3?

Summary:

The third term of a geometric progression with first term 3 and common ratio 3 is 27.