An arithmetic sequence is defined as a sequence of numbers in which each term after the first is formed by adding a constant difference, known as the common difference, to the previous term.
In the given sequence: 9, 11, 13, 15, we can observe that:
- The first term (a1) is 9.
- The common difference (d) is 2 (since 11 – 9 = 2, 13 – 11 = 2, and 15 – 13 = 2).
The formula for the nth term (an) of an arithmetic sequence can be expressed as:
an = a1 + (n – 1) * d
Substituting the values we have:
- a1 = 9
- d = 2
The equation becomes:
an = 9 + (n – 1) * 2
If we simplify this, we find:
an = 9 + 2n – 2
an = 2n + 7
Therefore, the equation for the nth term of the arithmetic sequence 9, 11, 13, 15 is:
an = 2n + 7
This means that you can find any term in this sequence by substituting the value of n into the equation.