An arithmetic progression has 5 as its first term and the last term is 60. If the sum of the terms is 195, then the common difference is :

In the arithmetic progression,

First term a = 5

Last term l = 60

Sum of the terms = 195

$$\Rightarrow$$  $$\frac{n}{2}$$(a+l) = 195

$$\Rightarrow$$  $$\frac{n}{2}$$(5 + 60) = 195

$$\Rightarrow$$  $$\frac{n}{2}$$(65) = 195

$$\Rightarrow$$   n = 6

Last term = 60

$$\Rightarrow$$  a + (n-1)d = 60

$$\Rightarrow$$  5 + (6-1)d = 60

$$\Rightarrow$$  5d = 55

$$\Rightarrow$$  d = 11

$$\therefore\ $$Common difference d = 11