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 7th term of an Arithmetic Progression is 19, i.e., 7th 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.