Question

Check whether –150 is a term of the AP : 11, 8, 5, 2 .......

Answer 1

For this A.P., $a = 11$ and $d = a_2 − a_1 = 8 − 11 = −3$
Let $−150$ be the nth term of this A.P.
We know that,
$a_n = a + (n-1)d$
$-150 = 11 + (n-1)(-3)$
$-150 = 11-3n+3$
$-164 = -3n$
$n = \frac {164}{3}$
Clearly, n is not an integer.

Therefore, $−150$ is not a term of this A.P.