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

Question

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

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Lucas Discussed

Find the first negative term of sequence

999, 995, 991, 987,

...

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

A P = 999, 995, 991, 987, ...

Here,

a = 999, d = 995 - 999 = - 4

a_{n} < 0

\Rightarrow a + (n - 1) d < 0

\Rightarrow 999 + (n - 1) (- 4) < 0

\Rightarrow 999 - 4 n + 4 < 0

\Rightarrow 1003 - 4 n < 0

\Rightarrow 1003 < 4 n

\Rightarrow \frac{1003}{4} < n

\Rightarrow n > 250.75

Nearest term greater than

250.75

251

So,

25 1^{s t}

term is the first negative term

Now, we will find the

25 1^{s t}

term

a_{n} = a + (n - 1) d

\Rightarrow a_{251} = 999 + (251 - 1) (- 4)

\Rightarrow a_{251} = 999 + 250 \times - 4

\Rightarrow a_{251} = 999 - 1000

\Rightarrow a_{251} = - 1

∴, - 1

is the first negative term of the given AP.

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Question Text	Find the first negative term of sequence $999, 995, 991, 987,$ $...$
Answer Type	Text solution:1
Upvotes	150