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

Solution:

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.

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 the 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.

Hence, the first term of an arithmetic progression can be found out by solving two equations found from the two given terms.

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

Summary:

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