Understanding sequences

Here, we’ll learn how to find missing terms in arithmetic and geometric sequences.

1. Arithmetic Sequences

An arithmetic sequence adds or subtracts the same amount each time. For example:

\[ 3, 6, \_, 12 \]

To find the missing term, work out the difference between terms. Here, \( 6 - 3 = 3 \), so we add 3 each time. The missing term is:

\[ 6 + 3 = 9 \]

The sequence is \( 3, 6, 9, 12 \).

2. Geometric Sequences

A geometric sequence multiplies or divides by the same number each time. For example:

\[ 2, \_, 8, 16 \]

To find the missing term, divide one term by the previous term. Here, \( \frac{16}{8} = 2 \), so we multiply by 2 each time. The missing term is:

\[ 2 \times 2 = 4 \]

The sequence is \( 2, 4, 8, 16 \).

Summary

• In arithmetic sequences, add or subtract the same amount to find missing terms.
• In geometric sequences, multiply or divide by the same number to find missing terms.