Question

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

Answer 1

For this A.P.,
a = 11
d = a2 − a1 
   = 8 − 11 = −3
Let −150 be the n th term of this A.P.

We know that,
an = a + (n − 1) d
-150 = 11 + (n - 1)(-3)
-150 = 11 - 3n + 3
-164 = -3n
n = 164/3
Clearly, n is not an integer.
Therefore, - 150 is not a term of this A.P.