Correct Answer - Option 3 : 3/2

__CONCEPT__**:**

- The nth term an of the AP with first term a and common difference d is given by an = a + (n – 1) d.

**CALCULATION****:**

Let’s ‘a’ be the first term and ‘d’ be the common difference.

Given that 7^{th} term of an Arithmetic Progression is 19, i.e., 7^{th} term = 19

⇒ a + (7 - 1) d = 19

⇒ a + 6d = 19 ....(i)

and 13th term of an Arithmetic Progression is 28

⇒ a + (13 - 1)d = 28

⇒ a + 12d = 28 ....(ii)

Now, subtract the equation (i) from (ii) we get,

6d = 9

\(\rm\Rightarrow d=\rm\frac{3}{2} \)

Hence, option (3) is the correct answer.