# Write an expression for the nth term of the sequence, 15, 12, 9, 6, …

An arithmetic progression is a sequence where the difference between every two consecutive terms is the same.

## Answer: The expression for the n^{th} term of the sequence, 15, 12, 9, 6, … is a_{n} = 18 - 3n

Let's look into the stepwise solution

**Explanation:**

For a given arithmetic sequence, the nth term of AP is calculated using the following expression:

a_{n} = a + (n - 1) d

Where,

- 'a' is the first term of the AP
- 'd' is the common difference
- 'n' is the number of terms
- 'a
_{n}' is the n^{th}term of the AP.

Let's find the nth term of the sequence, 15, 12, 9, 6, …

Here, a = 15, d = -3, n = n

Thus, substituting these values in the formula

a_{n} = a + (n - 1) d

⇒ a_{n} =_{ }15 + (n - 1) (-3)

⇒ a_{n} = 15 + 3 - 3n

⇒ a_{n} = 18 - 3n

Thus, the expression for the n^{th} term of the sequence, 15, 12, 9, 6, … is a_{n} = 18 - 3n.

We can use Cuemath's Online Arithmetic sequence calculator to find the arithmetic sequence using the first term and the common difference between the terms.