The 7th term of an arithmetic progression is 19 and 13th term of the

1.	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. - 3/22. 3/43. 3/24. 3/5
Answer» 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.

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. - 3/22. 3/43. 3/24. 3/5

Answer» 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.

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