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Question -

 If the 3_rd and the 9_th terms of an A.P. are 4 and − 8 respectively. Which term of this A.P. is zero.



Answer -

Given that,

3rd term, a3 = 4

and 9th term, a9 = −8

We know that,

an = a+(n−1)d

Therefore,

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 will get here,

−12 = 6d

d = −2

From equation (i), we can write,

4 = a+2(−2)

4 = a−4

a = 8

Let nth term ofthis A.P. be zero.

aa+(n−1)d

0 = 8+(n−1)(−2)

0 = 8−2n+2

2= 10

n = 5

Hence, 5th termof this A.P. is 0.

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