Is -150 a term of the A.P. 11, 8, 5, 2, … ?

1.	Is -150 a term of the A.P. 11, 8, 5, 2, … ?
Answer» Given, A.P. 11, 8, 5, 2, … Here, a = 11 and d = a₂ – a₁ = 8 – 11 = -3 We know that, n^th term a_n = a + (n – 1)d Required to check n^th term a_n = -150 a + (n – 1)d = -150 11 + (n – 1)(-3) = -150 11 – 3n + 3 = -150 3n = 150 + 14 3n = 164 ⇒ n = 164/3, which is not a whole number. Therefore, -150 is not a term in the A.P.

Answer»

Given, A.P. 11, 8, 5, 2, …

Here, a = 11 and d = a₂ – a₁ = 8 – 11 = -3

We know that, n^th term a_n = a + (n – 1)d

Required to check n^th term a_n = -150

a + (n – 1)d = -150

11 + (n – 1)(-3) = -150

11 – 3n + 3 = -150

3n = 150 + 14

3n = 164

⇒ n = 164/3, which is not a whole number.

Therefore, -150 is not a term in the A.P.

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