NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 3(iii)

Question:

In the following APs, find the missing terms in the boxes : 5, ?, ?, 9 1/2

Given:

An Arithmetic Progression (AP) with first term a = 5 and last term l = 912 = 192

To Find:

The missing terms in the AP.

Formula:

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

Solution:

Let the AP be 5, a₂, a₃, 192. 

Here, a = 5 and a₄ = 192.

Using the formula a_n = a + (n-1)d, 

we have a₄ = a + (4-1)d 

⇒ 192 = 5 + 3d.

Solving for d, 

we get 3d = 192 - 5 = 92 

⇒ d = 96 = 32 = 1.5

Therefore, 

a₂ = a + d 

⇒ a₂ = 5 + 1.5 

⇒ a₂ = 6.5 

and 

a₃ = a + 2d 

⇒ a₃ = 5 + 2(1.5) 

⇒ a₃ = 5 + 3 

⇒ a₃ = 8

Result:

The missing terms are 6.5 and 8.

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 3(iv)

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