Find the nth term 1 + 4 + 7 + 10 + 13 ⋯

We will use the concept of sequence and series in order to find the nth term.

Answer: nth-term a_n = 3n - 2

Let us see how we will use the concept of sequence and series in order to find the nth term.

Explanation:

This is an arithmetic sequence.

First-term a₁ = 1

Second-term a₂ = 4

Third-term a₃ = 7

Fourth term a₄ = 10

Difference between two terms = 3

As per arithmetic sequence formula, a_n = a + (n-1)d 

Here, a = 1, d = 3

 a_n = 1 + (n - 1)(3)

 a_n = 1 + 3n - 3

 a_n = 3n - 2

Thus, we can observe that nth-term a_n = 3n - 2