Question

If the 3e and the 94 terms of an AP are 4 and – 8 respectively, which term of this Ap zero?​

Answer 1

If the 3rd and 9th term are 4 and -8, respectively, Which term of an AP is zero?

Let first term of AP = a & common difference between any two consecutive terms = d

So, nth term of AP= a+(n-1)d

According to question,

3rd term= a+(3-1)d

= a + 2d=4 …….(1)

9th term= a+(9-1)d

= a+ 8d = - 8 ………(2)

Subtracting equation (1) from (2),

6d = - 12 => d= - 12/6

=> d = - 2

Putting the value of d in equation(1),

a + 2(-2) = 4

a = 4+4 =8

Let the pth term of AP be zero(0).

So, a + (p-1)d = 0

Putting the value of a and d in above equation

8 + ( p - 1) (-2) = 0

8 + ( - 2p + 2) = 0

10 - 2p = 0

2p = 10

p = 5

So, the fifth term of the AP is zero.