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

Question

Philoid · Accepted Answer

Here, First term = a = 11

Common difference = d = 8 - 11 = - 3

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

Since, n^th term of an AP is given by:

a_n = a + (n - 1)d

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

So, let a_n = - 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.