# How to find the first term of an arithmetic sequence when given two terms?

Arithmetic Progressions are sequences of numbers that have a common difference between a pair of consecutive numbers. Using certain properties and formulae, we can find the nth terms of arithmetic progressions as well as the sum of a certain number of terms. In this blog, we will find the first term of an arithmetic sequence when given two terms.

## Answer: The first term of an arithmetic progression can be found out by solving two equations found from the two given terms.

Let's understand the answer in detail.

**Explanation:**

Let's understand this with the help of an example.

Let's find the first term of the sequence whose 3^{rd} term is 15, and 7^{th} term is 35.

Let the first term be 'a' and the common difference be 'd'.

Using the formula to find nth term, we get:

⇒ a + (3 - 1)d = 15 ---- (1)

⇒ a + (7 - 1)d = 35 ---- (2)

Solving equations (1) and (2), we get d = 5 and a = 5.