# What is the 25th term of this arithmetic sequence 3, 9, 15, 21, 27, …?

A sequence in which the difference between all pairs of consecutive numbers is equal is called an arithmetic progression.

## Answer: The 25th term of the sequence that begins with 3 is 147.

Let's solve for the 25^{th} term of the arithmetic progression.

**Explanation:**

The given sequence is 3, 9, 15, 21, 27, …

It is an arithmetic progression so the common difference between all consecutive numbers is 6.

Let a_{1 }be the first term of the sequence and d be a common difference.

Therefore, a_{1} = 3 and d = 6.

For n^{th} term, the n^{th} term of the AP formula is a_{n} = a_{1} + (n - 1) d

⇒ a_{25} =_{ }3 + (25 - 1) 6

= 3 + 24 × 6

= 3 + 144

= 147