# How to find the n^{th} term of an arithmetic sequence?

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

## Answer: The expression to calculate the n^{th} term of an arithmetic sequence is a_{n} = a + (n - 1) d.

Let's look into the stepwise solution

**Explanation:**

For a given arithmetic sequence, the n^{th }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 take an example to understand this.

Example: Find the 25^{th} term of the given arithmetic sequence 3, 9, 15, 21, 27, …

Solution:

a = 3, d = 6, n = 25

Thus, substituting these values in the formula

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

⇒ a_{25} =_{ }3 + (25 - 1) 6

⇒ a_{25} = 3 + 24 × 6

⇒ a_{25} = 3 + 144

⇒ a_{25} = 147

Thus. the 25^{th} term of the given sequence is 144.

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.

### Hence, the expression to calculate the n^{th} term of AP if given by a_{n} = a + (n - 1) d.

visual curriculum