NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 16

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 16

Question:

Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

Given:

Third term (a3) = 16
Seventh term (a7) exceeds fifth term (a5) by 12. i.e., a7 =  a5  + 12

To Find:

The arithmetic progression (AP).

Formula:

The nth term of an AP is given by an = a + (n-1)d, where 

'a' is the first term and 

'd' is the common difference.

Solution:

We are given that a3 = 16. 

Using the formula, 

a3 = a + 2d = 16 

⇒ a + 2d = 16 (Equation 1)

Also, a7 = a5 + 12. 

Using the formula, 

(a + 6d) - (a + 4d) = 12 

⇒ 2d = 12 

⇒ d = 6

Substituting d = 6 in Equation 1: 

a + 2(6) = 16 

⇒ a + 12 = 16 

⇒ a = 4

Therefore, the AP is a, a+d, a+2d, a+3d... which is 4, 8, 12, 16, 20, 24, 28...

Result:

The arithmetic progression is 4, 8, 12, 16, 20, 24, 28...

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