Is - 150 a term of the AP 11, 8, 5, 2, ...?

Here, First term = a = 11

Common difference = d = 8 - 11 = - 3


Now, to check: - 150 is a term of the AP or not.


Since, nth term of an AP is given by:


an = a + (n - 1)d


If - 150 is a term of the AP, then it must satisfy this equation.


So, let an = - 150


∴ - 150 = 11 + (n - 1) × (-3)


⇒ - 150 - 11 = - 3n + 3


⇒ - 161 = - 3n + 3


⇒ - 161 - 3 = - 3n


⇒ 3n = 164


⇒ n = 164/3 = 54.66


But this is not possible because n is the number of terms which can’t be a fraction.


Therefore, - 150 is not a term of the given AP.


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