To find the nth term of the sequence 15, 12, 9, 6, we first need to identify the pattern in the numbers. Let’s analyze the sequence:
- 15 (1st term)
- 12 (2nd term)
- 9 (3rd term)
- 6 (4th term)
We can observe that each term in the sequence is decreasing by 3:
- 15 – 12 = 3
- 12 – 9 = 3
- 9 – 6 = 3
This indicates that the sequence is an arithmetic sequence where the first term (
a) is 15 and the common difference (
d) is -3.
The formula for the nth term (
a_n) of an arithmetic sequence is given by:
a_n = a + (n – 1) * d
Substituting the known values into the formula:
- a = 15
- n is the term number
- d = -3
We get:
a_n = 15 + (n – 1) * (-3)
Now, simplifying this:
- a_n = 15 – 3(n – 1)
- a_n = 15 – 3n + 3
- a_n = 18 – 3n
Thus, the expression for the nth term of the sequence 15, 12, 9, 6 can be concisely written as:
a_n = 18 – 3n
With this expression, you can substitute any value of n to find the corresponding term in the sequence.