Question

If the 3^rd and the 9^th 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, 5^th term of this A.P. is 0.