Question

If the 3rd and 9th terms of an AP are 4 and −8 respectively, then which term of the AP is 0?
(a) 5th
(b) 7th
(c) 11th
(d) 13th

Answer 1

( a) 5^th
T₃ = a + 2d = 4 ...(i)
T₉ = a + 8d = -8 ...(ii)
On subtracting (i) from (ii), we get:
⇒ 6d = -12
⇒ d = -2
Putting the value of d in (i), we get:
⇒ a - 4 = 4
⇒ a = 8
Let the T_n term be 0.
Then T_n = 0
⇒ ​a + (n - 1)d = 0
⇒ 8 + (n - 1) ⨯ (-2) = 0
⇒ 2n = 10
⇒ n = 5
Hence, the 5^th term of the AP is 0.