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

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#### Solution

For this A.P.,

a = 11

d = a_{2} − a_{1} = 8 − 11 = −3

Let −150 be the nth 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.

Concept: nth Term of an AP

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