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

Question:

The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Given:

First term (a) = 5
Last term (l) = 45
Sum of the AP (S_n) = 400

To Find:

Number of terms (n) and common difference (d)

Formula:

Sum of an AP: S_n = n 2 (a + l)
Last term of an AP: l = a + (n - 1)d

Solution:

Using the sum formula: 400 = n 2 (5 + 45) 

⇒ 400 = 25n 1  

⇒ n = 16

Using the last term formula: 45 = 5 + (16 - 1)d 

⇒ 40 = 15d 

⇒ d = 40 15  

⇒ d = 8 3  

⇒ d = 2.5

Result:

Number of terms (n) = 16
Common difference (d) = 2.5

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 6

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