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.