How to Find the Next Term of a Geometric Sequence

Precalculus · Sequences and series

How to Find the Next Term of a Geometric Sequence

Problem

3,\ 6,\ 12,\ 24,\ \ldots

Answer

48

In a geometric sequence each term is the previous term times a fixed ratio. Find the ratio, then multiply once more.

Step-by-step solution

Find the common ratio.
$\frac{6}{3} = 2$
Why: A geometric sequence multiplies by the same number each time.
Check the ratio with another pair.
$\frac{24}{12} = 2$
Why: The ratio must be the same between every pair of neighbouring terms.
Multiply the last term by the ratio.
$24 \times 2 = 48$
Why: The next term repeats the same multiplication.

Common mistakes

Adding 2 instead of multiplying by 2.
Finding the ratio backwards: 3/6 = 1/2.
Stopping after the first pair without checking the ratio holds.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

$2,\ 6,\ 18,\ \ldots$

Show answer

$54$
$1,\ 4,\ 16,\ \ldots$

Show answer

$64$
$5,\ 10,\ 20,\ \ldots$

Show answer

$40$
$3,\ 9,\ 27,\ \ldots$

Show answer

$81$
$8,\ 4,\ 2,\ \ldots$

Show answer

$1$