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given a series 1,2,2,3,3,3,4,4,4,4... if this cintinues then

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anik89
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given a series 1,2,2,3,3,3,4,4,4,4... if this cintinues then [#permalink] New post   10 Dec 2015, 20:33
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given a series 1,2,2,3,3,3,4,4,4,4... if this continues then what will be the value of 100th term?
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soumya1989
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Re: given a series 1,2,2,3,3,3,4,4,4,4... if this cintinues then [#permalink] New post   11 Dec 2015, 00:17
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Even though the options are not given, the answer is 45.

Explanation


This problem can be simplified in the following:

\(1 + 2 + 3 + .... + n >= 1000\)
\(or, (n)(n+1)/2 >= 1000\)

After some trials you have to find the n for which the LHS of the above equation just becomes larger than 1000. In this case n is 45. Thats the answer .
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Re: given a series 1,2,2,3,3,3,4,4,4,4... if this cintinues then [#permalink] New post   11 Dec 2015, 19:02
soumya1989 wrote:
Even though the options are not given, the answer is 45.

Explanation


This problem can be simplified in the following:

\(1 + 2 + 3 + .... + n >= 1000\)
\(or, (n)(n+1)/2 >= 1000\)

After some trials you have to find the n for which the LHS of the above equation just becomes larger than 1000. In this case n is 45. Thats the answer .


but the ans says 14.

1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,......................14,14,14,14,14,14,14,14,14,14,14,14,14,14

is there any formula?
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Re: given a series 1,2,2,3,3,3,4,4,4,4... if this cintinues then [#permalink] New post   12 Dec 2015, 06:29
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Hello Anik,
I made a silly mistake. Instead of 100 i took 1000. Apply the same logic you will see the answer becomes 14.
Soumya
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Re: given a series 1,2,2,3,3,3,4,4,4,4... if this cintinues then [#permalink] New post   12 Dec 2015, 20:25
soumya1989 wrote:
Hello Anik,
I made a silly mistake. Instead of 100 i took 1000. Apply the same logic you will see the answer becomes 14.
Soumya


i got the ans but could you please explain a little bit about this formula? its basically the formula of sum of first n terms . how this formula works here??
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Re: given a series 1,2,2,3,3,3,4,4,4,4... if this cintinues then [#permalink] New post   06 Jan 2016, 05:35
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1,2,3,4,5,6,7,8,9,10,11,12,13,14,15...
1,2,2,3,3,3,4,4,4,4,5,5,5,5,5...

n=3>> n(n+1)/2=6
n=4>> n(n+1)/2=10
n=5>> n(n+1)/2=15

in this series, in fact n(n+1)/2 is the greatest value for n(th) term.

for example: for 9th term >> n(n+1)/2 >= 9 >> for n=3 we can not reach to 9th term, we need to consider 4 for n.

so for 100th >> n(n+1)/2>=100 >> 14*15=210 so n=14.
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Re: given a series 1,2,2,3,3,3,4,4,4,4... if this cintinues then [#permalink]
06 Jan 2016, 05:35
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