Question

How do you find the common ratio of a geometric sequence if given the first term and fourth term​?

Answer 1

To find the common ratio of a geometric sequence, divide the fourth term by the first term and take the cube root of the result.

Step-by-step explanation:

To find the common ratio of a geometric sequence when given the first term (a1) and the fourth term (a4), you can use the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1).

Since you have the first and fourth terms, your equation will look like this:
a4 = a1 × r3. To solve for the common ratio (r), you would divide the fourth term by the first term and then take the cube root of that result. Here are the steps:

1. Divide the fourth term by the first term: ratio = a4 / a1.
2. Take the cube root of the ratio to find the common ratio: r = ∛(ratio).

You do not need a calculator or computer to find the common ratio, and you do not need to write a linear equation. The process involves straightforward arithmetic operations.