# The 7th term of an arithmetic progression is 19 and 13th term of the same arithmetic progression is 28.Find the common difference of the arithmetic p

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The 7th term of an arithmetic progression is 19 and 13th term of  the same arithmetic progression is 28.Find the common difference of the arithmetic progression.

1. - 3/2
2. 3/4
3. 3/2
4. 3/5
5. None of these

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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.