NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 7

Question:

Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

Given:

Common difference (d) = 7
22^nd term (a₂₂) = 149

To Find:

Sum of first 22 terms (S₂₂)

Formula:

a_n = a + (n-1)d
S_n = n2(2a + (n-1)d)

Solution:

We have a₂₂ = 149 and d = 7. Using the formula a_n = a + (n-1)d, we get:

149 = a + (22-1)7 

⇒ 149 = a + 147 

⇒ a = 149 - 147 

⇒ a = 2

Now, we use the formula for the sum of an AP:

S_n = n2(2a + (n-1)d)

Substituting n = 22, a = 2, and d = 7, we get:

⇒ S₂₂ = 222(2(2) + (22-1)7) 

⇒ S₂₂ = 11(4 + 147) 

⇒ S₂₂ = 11(151) 

⇒ S₂₂ = 1661

Result:

The sum of the first 22 terms is 1661.

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NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 8

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