Find the first negative term of sequence 999, 995, 991, 987, ...

1.	Find the first negative term of sequence 999, 995, 991, 987, ...
Answer» AP = 999, 995, 991, 987,… Here, a = 999, d = 995 – 999 = –4 a_n < 0 ⇒ a + (n – 1)d < 0 ⇒ 999 + (n – 1)(–4) < 0 ⇒ 999 – 4n + 4 < 0 ⇒ 1003 – 4n < 0 ⇒ 1003 < 4n ⇒ 1003/4 < n ⇒ n > 250.75 Nearest term greater than 250.75 is 251 So, 251^st term is the first negative term Now, we will find the 251^st term a_n = a +(n – 1)d ⇒ a₂₅₁ = 999 + (251 – 1)(–4) ⇒ a₂₅₁ = 999 + 250 × –4 ⇒ a₂₅₁ = 999 – 1000 ⇒ a₂₅₁ = – 1 ∴, –1 is the first negative term of the given AP.

Answer»

AP = 999, 995, 991, 987,…

Here, a = 999, d = 995 – 999 = –4

a_n < 0

⇒ a + (n – 1)d < 0

⇒ 999 + (n – 1)(–4) < 0

⇒ 999 – 4n + 4 < 0

⇒ 1003 – 4n < 0

⇒ 1003 < 4n

⇒ 1003/4 < n

⇒ n > 250.75

Nearest term greater than 250.75 is 251

So, 251^st term is the first negative term

Now, we will find the 251^st term

a_n = a +(n – 1)d

⇒ a₂₅₁ = 999 + (251 – 1)(–4)

⇒ a₂₅₁ = 999 + 250 × –4

⇒ a₂₅₁ = 999 – 1000

⇒ a₂₅₁ = – 1

∴, –1 is the first negative term of the given AP.

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