NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 20

Question:

Ramkali saved Rs 5 in the first week of a year and then increased her weekly savings by Rs 1.75. If in the nth week, her weekly savings become Rs 20.75, find n.

Given:

First week savings (a) = Rs 5
Common difference (d) = Rs 1.75
nth week savings = Rs 20.75

To Find:

The value of n (number of weeks).

Formula:

n^th term of an AP = a + (n-1)d, where 

'a' is the first term and 

'd' is the common difference.

Solution:

We have 

a = 5, 

d = 1.75, and 

a_n = 20.75. 

Substituting these values into the formula: a_n = a + (n-1)d

⇒ 20.75 = 5 + (n-1)1.75 

⇒ 15.75 = (n-1)1.75

⇒ 15.75 1.75 = n-1

9 = n - 1 

⇒ n = 9 + 1 

⇒ n = 10

Let's verify: 

a₁₀ = 5 + (10-1)1.75 

⇒ a₁₀ = 5 + 9(1.75) 

⇒ a₁₀ = 5 + 15.75 

⇒ a₁₀ = 20.75. 

This is correct.

Result:

Therefore, n = 10

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Example 11

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