Question

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

Answer 1

Given that, $a_3 = 4$ and $a_9 = −8$
We know that, $a_n = a + (n − 1) d$
$a_3 = a + (3 − 1) d$
$4 = a + 2d$ ..…(i)
$a_9 = a + (9 − 1)$ 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 nth 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, 5th term of this A.P. is 0.