NCERT Class X Chapter 5: Arithmetic Progression Example 5

NCERT Class X Chapter 5: Arithmetic Progression Example 5

Question:

Determine the AP whose 3rd term is 5 and the 7th term is 9.

Given:

3rd term (a3) = 5

7th term (a7) = 9

To Find:

The arithmetic progression (AP).

Formula:

an = a1 + (n-1)d

where,

an is the nth term, 

a1 is the first term, and 

d is the common difference.

Solution:

We have 

a3 = a1 + 2d = 5 and 

a7 = a1 + 6d = 9.

Subtracting the first equation from the second equation, we get:

(a1 + 6d) - (a1 + 2d) = 9 - 5 

a1 + 6d - a1 - 2d = 9 - 5 

⇒ 6d - 2d = 4 

⇒ 4d = 4

⇒ d = 1

Substituting d = 1 into a1 + 2d = 5, 

we get: a1 + 2(1) = 5 

⇒ a1 = 3

Therefore, the AP is 3, 4, 5, 6, 7, 8, 9, ...

Result:

The arithmetic progression is 3, 4, 5, 6, 7, 8, 9, ...

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