Question

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

If the 3rd and the 9th terms of an arithmetic progression are 4 and -8 respectively, Which term of it is zero?

Answer 1

Given that,

a₃ = 4

a₉ = −8

We know that,

a_n = a + (n − 1) d

a₃ = a + (3 − 1) d

4 = a + 2d               ...(I)

a₉ = a + (9 − 1) d

−8 = a + 8d                ...(II)

On subtracting equation (I) from (II), we obtain

−12 = 6d

d = −2

From equation (I), we obtain

4 = a + 2 (−2)

4 = a − 4

a = 8

Let n^th term of this A.P. be zero.

a_n = a + (n − 1) d

0 = 8 + (n − 1) (−2)

0 = 8 − 2n + 2

2n = 10

n = 5

Hence, 5^th term of this A.P. is 0.