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

Question

KnowledgeBoat · Accepted Answer

Here, a₂ - a₁ = 8 - 11 = -3, a₃ - a₂ = 5 - 8 = -3, a₄ - a₃ = 2 - 5 = -3 i.e. any term - preceding term = -3, a fixed number. So, the given list of numbers forms an A.P. with a = 11 and d = -3. Now we want to find whether there exists a natural number n for which a_n = -150 ⇒ a + (n - 1)d = -150 ⇒ 11 + (n - 1)(-3) = -150 ⇒ 11 - 3n + 3 = -150 ⇒ 14 - 3n = -150 ⇒ 3n = 14 + 150 ⇒ 3n = 164 ⇒ n = , which is not a natural number. Hence, there is no term in the given list of numbers which is -150.

Mathematics

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

AP GP

Related Questions

If the first term of an A.P. is -18 and its 10th term is zero, then find its common difference.

Find whether 55 is a term of the A.P. 7, 10, 13, …. or not. If yes find which term is it.

Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.