Question

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

Answer 1

The given AP is 11, 8, 5, 2, ...

Here, a = 11and d = 8 – 11 = –3

Let the nth term of the given AP be –150. Then,

a_n = –150

⇒ 11 + (n – 1) × (–3) = –150   ...[a_n = a + (n – 1)d]

⇒ –3n +14 = –150

⇒ –3n = –164

⇒ n = `164/3 = 54 2/3`

But, the number of terms cannot be a fraction.

Hence, –150 is not a term of the given AP.