If the 3rd and the 9th terms of an A.P. are 4 and − 8 respectively. Which term of this A.P. is zero.
Given that,
a3 = 4
a9 = −8
We know that,
an = 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 get,
−12 = 6d
d = −2
From equation (i), we get,
4 = a + 2 (−2)
4 = a − 4
a = 8
Let nth term of this A.P. be zero.
an = 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.
