If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, wh

1.	If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
Answer» Solution: Given, a3 = 4 and a9 = - 8 a3 = a + 2d = 4 a9 = a + 8d = - 8 Subtracting 3rd term from 9th term, we get; a + 8d – a – 2d = - 8 – 4 = - 12 Or, 6d = - 12 Or, d = - 2 Substituting the value of d in 3rd term, we get; a + 2(-2) = 4 Or, a – 4 = 4 Or, a = 8 Now; 0 = a + (n – 1)d Or, 0 = 8 + (n – 1)(- 2) Or, (n – 1)(- 2) = - 8 Or, n – 1 = 4 Or, n = 5 Thus, 5th term of this AP is zero.

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

Answer»

Solution: Given, a3 = 4 and a9 = - 8

a3 = a + 2d = 4

a9 = a + 8d = - 8

Subtracting 3rd term from 9th term, we get;

a + 8d – a – 2d = - 8 – 4 = - 12

Or, 6d = - 12

Or, d = - 2

Substituting the value of d in 3rd term, we get;

a + 2(-2) = 4

Or, a – 4 = 4

Or, a = 8

Now; 0 = a + (n – 1)d

Or, 0 = 8 + (n – 1)(- 2)

Or, (n – 1)(- 2) = - 8

Or, n – 1 = 4

Or, n = 5

Thus, 5th term of this AP is zero.