6. Check whether - 150 is a term of the AP: 11,8,5,2

1.	6. Check whether - 150 is a term of the AP: 11,8,5,2
Answer» Here, a = 11 d = 8 - 11 = - 3 Let - 150 be the nth term of the given A.P. We know that, an = a + (n - 1)d ⇒ - 150 = 11 + (n - 1) - 3 ⇒ - 150 = 11 - 3n + 3 ⇒ (- 150) + (- 14) = - 3n ⇒ - 3n = - 164 ⇒ 3n = 164 ⇒ n = 164/3 So, it is clear that n is not an integer. Therefore, - 150 is not a term of the given A.P.

Answer»

Here,

a = 11

d = 8 - 11 = - 3

Let - 150 be the nth term of the given A.P.

We know that,

an = a + (n - 1)d

⇒ - 150 = 11 + (n - 1) - 3

⇒ - 150 = 11 - 3n + 3

⇒ (- 150) + (- 14) = - 3n

⇒ - 3n = - 164

⇒ 3n = 164

⇒ n = 164/3

So, it is clear that n is not an integer.

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

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