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

Solution:

The formula for n^th term of an AP is aₙ = a + (n - 1) d

Here, aₙ is the n^th term, a is the first term, d is the common difference and n is the number of terms.

3^rd term of the AP = 4

a₃ = a + (3 - 1)d = 4

a + 2d = 4 .... (1)

9^th term of the AP = - 8

a₉ = a + (9 - 1)d = - 8

a + 8d = - 8 ....(2)

Solving (1) and (2) for a and d

a + 2d - (a + 8d) = 4 - (- 8)

- 6d = 12

d = - 2

Putting d = - 2 in equation (1)

a + 2 × (- 2) = 4

a - 4 = 4

a = 8

Now, by using the values of a and d, we will find the term for which the value is 0.

a + (n - 1)d = 0

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

n - 1 = 4

n = 5

Thus, 5^th term of the AP will be 0.

☛ Check: NCERT Solutions Class 10 Maths Chapter 5

Video Solution:

NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 9

Summary:

If the 3^rd and the 9^th terms of an AP are 4 and - 8 respectively, 5^th term of the AP will be zero.

☛ Related Questions:

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