Steps to find the nth term
Step 1: At first find the first and 2nd term, that is a1 and a2.
Step 2: Then find the common difference between them, that is d = (a2-a1)
Step 3: Now, by adding the difference d with the 2nd term we will get 3rd term, and like this, the series goes on. That is 2nd term, a2 = a1+d (a1 is first term)
3rd term, a3 = a2+d = (a1+d) +d = a1+2d
4th term, a4 = a3+d = (a1+2d) +d = a1+3d
So, we can see that the number of d is 1 less than the number of terms. That is,
In a2, the number of d is 1, [(2-1) = 1]
In a3 the number of d is 2, [(3-1) = 2]
In a4 the number of d is 3, [(4-1) = 3]
So, similarly, for the Nth term, the number of d must be (N-1) times.
Therefore, Nth term, an = a1 + (N-1)d ⇢ [First term + (Last term – 1)×common difference]