The common difference in the arithmetic sequence 6, 10, 14, 18 is 4.
Understanding Arithmetic Sequences
An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant. This constant difference is called the common difference. To find the common difference, simply subtract any term from the term that immediately follows it.
- Example: In the sequence 6, 10, 14, 18:
- 10 - 6 = 4
- 14 - 10 = 4
- 18 - 14 = 4
The common difference is consistently 4.
The General Term of an Arithmetic Sequence
The general term (or nth term) of an arithmetic sequence can be expressed using the formula: a<sub>n</sub> = a<sub>1</sub> + (n-1)d, where:
a<sub>n</sub>is the nth terma<sub>1</sub>is the first termnis the term numberdis the common difference
For the given sequence (6, 10, 14, 18), a<sub>1</sub> = 6 and d = 4. Therefore, the general term is a<sub>n</sub> = 6 + (n-1)4.
This formula allows you to calculate any term in the sequence. For instance, to find the 5th term:
a<sub>5</sub> = 6 + (5-1)4 = 6 + 16 = 22
As evidenced by the provided references, identifying the common difference is fundamental to understanding and working with arithmetic sequences. The common difference is the key to calculating other terms and understanding the overall pattern.
