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

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

Question:

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Question:

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Given:

Second term (a2) = 14
Third term (a3) = 18

To Find:

Sum of first 51 terms (S51)

Formula:

an = a + (n-1)d
Sn = n 2 (2a + (n-1)d)

Solution:

Common difference (d) = a3 - a2 = 18 - 14 = 4

a2 = a + d 

⇒ 14 = a + 4 

⇒ a = 10

S51 = 51 2 (2(10) + (51-1)4)

⇒ S51 = 51 2 (20 + 200) 

⇒ S51 = 51 2 (220) 

⇒ S51 = 51 × 110 

⇒ S51 = 5610

Result:

The sum of the first 51 terms is 5610.

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