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How to find the nth term an Arithmetic progression

Question 

Find the number of terms in an Ap given that its first and last terms are a and 37a respectively and that its common difference is 4a.

Solution

nth term of AP

Tn = a +(n-1)d

From the question

First term a = a

Last term Tn = 37a

Common difference d = 4a

Number of terms n =?

Substitute a, Tn and d into the nth term formula

Tn = a +(n-1)d

37a = a +(n-1)4a

Collect like terms

37a-a = (n-1)4a

36a = (n-1)4a

Divide through by 4a

36a/4a = (n-1)4a/4a

9 = n-1

make n subject formula

n = 9+1

n = 10

The AP as 10 terms

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