Question

Which term of the AP : $121,117,113,...$, is its first negative term
[Hint : Find $n$ for $a_n<0$]

Answer 1

Given A.P is $121,117,\mathrm{113...............}$

$a=121$ and $d=117-121=-4$

$a_n=a+(n-1)d$

$=121+(n-1)(-4)$

$=121-4n+4$

$=125-4n$

We have find the first term of this A.P.

Therefore $a_n<0$

$125-4n<0$

$124<4n$

$n>\frac{125}{4}$

$n>31.25$

$n=32$