Question

Which term of the AP: 121, 117, 113, ..... is its first negative term?

Answer 1

Given A.P. is $121, 117, 113 ……$
$a = 121$ and $d = 117 − 121 = −4$
$a_n = a + (n − 1) d$
$a_n = 121 + (n − 1) (−4)$
$a_n= 121 − 4n + 4$
$a_n= 125 − 4n$
We have to find the first negative term of this A.P.
Therefore, $an < 0$
$125 - 4n < 0$
$125 < 4n$
$n > \frac {125}{4}$
$n > 31.25$

Therefore, 32nd term will be the first negative term of this A.P.