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

Question:

In the following APs, find the missing terms in the boxes : ?,38,?,?,?,-22

Given:

An arithmetic progression (AP) with the known term 38 and -22.

To Find:

The missing terms in the given 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 a₁, a₂, a₃, a₄, a₅, a₆. 

We are given that a₂ = 38 and a₆ = -22.

Using the formula a_n = a + (n-1)d, we have:

a₂ = a + d = 38 

⇒ a = 38 - d

a₆ = a + 5d = -22

Substituting a = 38 - d into a₆ = a + 5d = -22, we get:

(38 - d) + 5d = -22 

⇒ 4d = -60 

⇒ d = -15

Now, we find 'a': 

a = 38 - d 

⇒ a = 38 - (-15) 

⇒ a = 38 + 15

⇒ a = 53

Therefore, the AP is: 53, 38, 23, 8, -7, -22

Result:

The missing terms are 53, 23, 8, -7

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 4

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