Question

Determine which term of the $A:P.121,117,113,.......$ is its first negative term?

Answer 1

Considering the series to be,

$121,117,113,......$

$a=121,d=117-121=113-117=-4$

For $a_n$ to be negative

$a_n<0$

$a+(n-1)d<0$

$121+(n-1)(-4)<0$

$(n-1)(-4)>121$

$4n>125$

$n>31.25$

$n=32$

Therefore the 31st term is the negative term.

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

$a_n=121+(32-1)(-4)$

$a_n=121-124$

$a_n=-3$