9. 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, 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 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.