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

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

Question

In an AP: given a = 8, an = 62, Sn = 210, find n and d.

Given

a = 8, an = 62, Sn = 210

To Find

n and d

Formula

The nth term of arithmetic progression is given by an = a + (n-1)d
Sum of an arithmetic progression = Sn = n 2 (2a + (n-1)d)

Solution

Using an = a + (n-1)d 

⇒ 62 = 8 + (n-1)d 

⇒ (n-1)d = 54 ...(1)

Using Sn = n 2 (2a + (n-1)d) 

⇒ 210 = n 2 (16 + 54) 

⇒ 420 = 70n 

⇒ n = 6

Substituting n = 6 in (1): (6-1)d = 54 

⇒ 5d = 54 

⇒ d = 54 5  

= 9

Result

n = 6, d = 9

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