Check whether -150 is a term of the A.P. 11, 8, 5, 2, …

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Solution

$F o r t h i s A . P, a = 11 d = a_{2} - a_{1} = 8 - 11 = - 3 L e t - 150 b e t h e n^{t h} t e r m o f t h i s A . P . W e k n o w t h a t, a_{n} = a + (n - 1) d - 150 = 11 + (n - 1) (- 3) - 164 = - 3 n n = \frac{164}{3}$
Clearly, n is not an integer.
Therefore, - 150 is not a term of this A.P.

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