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

a₃ = 4, a₉ = -8, a_n = 0, n =? 

a₃ = a + 2d = 4 ………….. (1) 

a₉ = a + 8d = -8 …………. (2) 

From equation (1) – equation (2).

∴ d = -2 

a + 2d = 4 

a – 2(2) = 4 

a – 4 =4 

∴ a = 4 + 4 

∴ a = 8 

a_n = a + (n – 1) d 

= 8 + (n – 1) (-2) 

= 8 – 2n + 2 

= 10 – 2n = 0 

∵ a_n = 0

∴ n = \(\frac{10}{2}\)

∴ n = 5 

∴ 5^th term of this AP is Zero.