An arithmetic progression or arithmetic sequence is a number’s sequence such that the difference between the consecutive terms is constant.

Solutions:

(iii) Given, A.P. $11,8,5,2$ …

Here, $a=11$ and $d={{a}_{2}}-{{a}_{1}}=8-11=-3$

We know that, ${{n}^{th}}$ term ${{a}_{n}}=a+\left( n-1 \right)d$

Required to check ${{n}^{th}}$ term ${{a}_{n}}=-150$

$a+\left( n-1 \right)d=-150$

$11+\left( n-1 \right)\left( -3 \right)=-150$

$11-3n+3=-150$

$3n=150+14$

$3n=164$

⇒ $n=164/3,$ which is not a whole number.

Therefore, $-150$ is not a term in the A.P.