Find the terms when the sequence are increasing. Why the common difference should be negative, why it is important to note if the terms of the sequence are increasing

Class 10th Maths, EXERCISE 5.2, Page No:106, Questions No:6.

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

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Here, a = 11 and d = 8 – 11 = – 3.

Let, the nth term of the A.P. is – 150.

Therefore, a_n = – 150

⇒ a + (n – 1)d = – 150

⇒ 11 + (n – 1)(- 3) = – 150

⇒ 11 – 3n + 3 = – 150

⇒ – 3n = – 164

⇒ n = 164/3 = 54(2/3)

Here, n is not a natural number, therefore, – 150 is not the term of A.P., 11, 8, 5, 2 . . .