Question

Which term of the A.P $122,116,110,.......$ is the first negative terms?

Answer 1

AP is 122,116,110.....

The nth term of an AP is given by

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

here, $a=122$

$d=116-122=-6$

Let the nth term of the AP be its first negative term

$a_n<0$

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

$122+(n-1)(-6)<0$

$122-6n+6<0$

$128<6n$

$6n>128$

$n>\frac{128}{6}$

$n>21.33$

Since the first negative term is greater than 21.22

So, it is 22nd term.