NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question3(v)

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 3 (v)

Question

In an AP: given d = 5, S9 = 75, find a and a9.

Given

d = 5, S9 = 75

To Find

a and a9

Formula

Sum of an arithmetic progression = Sn = n 2 [2a + (n - 1)d]

The nth term of arithmetic progression is given by an = a + (n - 1)d

Solution

Using the formula for the sum of an AP, Sn = n 2 [2a + (n - 1)d], we have:

S9 = 9 2 [2a + (9 - 1)5] = 75

⇒ 9[2a + 40] = 150

⇒ 2a + 40 = 150 9 = 50 3

⇒ 2a = 50 3 - 40 

= 50 - 120 3  

= -70 3

⇒ a = -35 3

Now, a9 = a + (9 - 1)d 

= a + 8d 

= -35 3 + 8(5) 

= -35 + 40 3  

= 5 3

Result

a = -35 3 , a9 = 5 3

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