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# In a certain sequence, the first term is -4, and every term

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In a certain sequence, the first term is -4, and every term [#permalink]  19 Apr 2018, 14:33
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In a certain sequence, the first term is -4, and every term thereafter is defined by $$2 * |x| * \frac{1}{2}$$, where x = preceding term. What is the sum of the first 300 terms?

A. It cannot be determined from the information given.

B. 0

C. 1186

D. 1192

E. 1200
[Reveal] Spoiler: OA

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Re: In a certain sequence, the first term is -4, and every term [#permalink]  19 Apr 2018, 18:06
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First term is given as -4

The subsequent terms in the sequence can be obtained by applying the formula 2*|x|*1/2 where x is the previous term.

If you notice carefully, you will see that

2 *|x| * 1/2 is nothing but |x|

So,
the first term is -4
Second term is |-4| = 4
Third term is |4| = 4
Fourth term is |4| = 4

and so on....

So, the sequence here is
-4, 4, 4, 4, ................. 4 (total 300 terms)

The first two terms cancel out with each other. (-4 + 4 = 0)
We are now left with 298 terms, and all the terms are equal to 4

Sum of these would be 298 * 4 = 1192

Hope this helps
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Re: In a certain sequence, the first term is -4, and every term [#permalink]  20 Apr 2018, 01:57
First term in the sequence is -4 and all other 299 terms are 4s

So 299*4 - 4

=1196-4
=1192

Re: In a certain sequence, the first term is -4, and every term   [#permalink] 20 Apr 2018, 01:57
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