Question

Find whether - 150 is a term of the AP 17, 12, 7, 2 .......?

Answer 1

The given A. P. is $17,12,7,2,.......$
First term, $a=17$
Common difference, $d=12-17=-5$
If $-150$ is a term of the given A.P., then for a natural number $n$, $a_n$ $=-150$
$\Rightarrow$ $a+(n-1)d=-150$
$\Rightarrow$ $17+(n-1)(-5)=-150$
$\Rightarrow$ $(-5)(n-1)=-150-17=-167$

$\Rightarrow n-1=\frac{167}{5}$

$\Rightarrow n=\frac{167}{5}+1=\frac{172}{5}=34.4$

Now, $34.4$ is not a natural number.
Thus, $-150$ is not a term of the A.P, $17,12,7,2..........$