NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 9

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 9

Question:

If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?

Given:

3rd term (a3) = 4
9th term (a9) = -8

To Find:

The term of the AP which is zero.

Formula:

an = a + (n-1)d, where an is the nth term, a is the first term, n is the number of terms, and d is the common difference.

Solution:

a3 = a + 2d = 4 ⇒ a = 4 - 2d

a9 = a + 8d = -8

Substitute a = 4 - 2d into a9:

(4 - 2d) + 8d = -8 ⇒ 6d = -12 ⇒ d = -2

Substitute d = -2 into a = 4 - 2d:

a = 4 - 2(-2) = 8

Let an = 0

0 = 8 + (n-1)(-2)

2(n-1) = 8

n - 1 = 4

n = 5

Result:

The 5th term of this AP is zero.

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