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

Question:

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Given:

First term (a) = 17
Last term (l) = 350
Common difference (d) = 9

To Find:

Number of terms (n) and sum of terms (S_n)

Formula:

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

Solution:

Using the formula l = a + (n - 1)d:

350 = 17 + (n - 1)9 

⇒ 350 - 17 = (n - 1)9 

⇒ 333 = (n - 1)9 

⇒ 333 9 = n - 1 

⇒ 37 = n - 1 

⇒ n = 38

Using the formula S_n = n(a + l) 2 :

⇒ S₃₈ = 38(17 + 350) 2  

⇒ S₃₈ = 38(367) 2  

⇒ S₃₈ = 19(367) 

⇒ S₃₈ = 6973

Result:

Number of terms (n) = 38
Sum of terms (S_n) = 6973

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

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