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The first three numbers on a certain list are 7, 8, and 9. Starting wi

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Carcass
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The first three numbers on a certain list are 7, 8, and 9. Starting wi [#permalink] New post   14 Mar 2022, 03:00
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The first three numbers on a certain list are 7, 8, and 9. Starting with the fourth number on the list, each number is the sum of the three that immediately precede it. If the nth number on the list is the first to exceed 200, what is the value of n?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
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Re: The first three numbers on a certain list are 7, 8, and 9. Starting wi [#permalink] New post   14 Mar 2022, 10:34
Carcass wrote:
The first three numbers on a certain list are 7, 8, and 9. Starting with the fourth number on the list, each number is the sum of the three that immediately precede it. If the nth number on the list is the first to exceed 200, what is the value of n?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11


I got the solution through hard calculation, is there an way to sole it using equations or something
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Re: The first three numbers on a certain list are 7, 8, and 9. Starting wi [#permalink] New post   14 Mar 2022, 10:54
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OE


The fourth number and numbers after it will be: 24, 41, 74, 139, 254. The 8th number, 254, is the first to exceed 200.
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Re: The first three numbers on a certain list are 7, 8, and 9. Starting wi [#permalink] New post   14 Mar 2022, 11:36
Carcass wrote:
OE


The fourth number and numbers after it will be: 24, 41, 74, 139, 254. The 8th number, 254, is the first to exceed 200.


Thanks Carcass, is there no other way to calculate this. What if we were asked first no. to exceed 2000 or something greater.
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Re: The first three numbers on a certain list are 7, 8, and 9. Starting wi [#permalink] New post   14 Mar 2022, 11:38
Thanks Carcass, I totally misread the question.
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Re: The first three numbers on a certain list are 7, 8, and 9. Starting wi [#permalink] New post   14 Mar 2022, 11:43
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AkkuJi wrote:
Carcass wrote:
OE


The fourth number and numbers after it will be: 24, 41, 74, 139, 254. The 8th number, 254, is the first to exceed 200.


Thanks Carcass, is there no other way to calculate this. What if we were asked first no. to exceed 2000 or something greater.


Probably there will be some sort of twist such as the number nth will be a multiple of some sort of cyclicity in the pattern.

If the question would as it is above but with a number over 2000 I do not see another way to go ahead and count as we did for just above 200.

But usually when we deal with huge numbers there is always some sort of other element to take into account not just a counting as above which is usually used for small numbers
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Re: The first three numbers on a certain list are 7, 8, and 9. Starting wi [#permalink] New post   14 Mar 2022, 11:57
Hmm yup make sense, they will be providing us some more clues if no. is going to be greater
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