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1, 1, 2, 3, 5, 8, 13, 21, 34, . . .

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Carcass
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1, 1, 2, 3, 5, 8, 13, 21, 34, . . . [#permalink] New post   07 Sep 2022, 00:09
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1, 1, 2, 3, 5, 8, 13, 21, 34, . . .


Quantity A
Quantity B
the 11th term in the sequence
90



A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

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B
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B
AkmKawser
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1, 1, 2, 3, 5, 8, 13, 21, 34, . . . [#permalink] New post   07 Sep 2022, 01:45
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F11=F9+F10 = 34+55 = 89
Thus Quantity B is Greater. Answer: B


The answer is B and it's simple. But I want to give a detailed explanation of this so that other similar problems can be tackled. So here we go.

1st of all this is neither a Geometric nor Arithmetic Sequence so we can't use any of those tricks here. We have to build it using the basic concept of defining Sequences.
If we think of it in an inductive way :
We have to think about it in a bottom-up manner. We have to think about it in terms of the 1st term and start building up to the bottom until we reach F11.

F3=F1+F2
F4=F2+F3
F5=F3+F4
....
F11 = F9+F10

If we think of it in a deductive way:
We have to think in a top-down manner. Breaking the actual problem into previous terms. So we start with F11 right away.
F11 =F9+F10
= {(F7+F8)+(F8+F9)}
= .........until we reach the base case.

In either case, the formula is simple as I have shown.
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steveharvi
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Re: 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . [#permalink] New post   26 Apr 2024, 07:04
According to me it is B, the gap between the terms of this sequence is 0, then 1 ,then 3, then 5 i.e. increasing by odd numbers; after 34 it is 47(+13) then it is 62(+15). Is this approach correct?
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Re: 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . [#permalink] New post   26 Apr 2024, 08:11
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Yes it is B

Correct both the answer and the approach
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sgatev23
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Re: 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . [#permalink] New post   10 Dec 2024, 04:01
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AkmKawser wrote:
F11=F9+F10 = 34+55 = 89
Thus Quantity B is Greater. Answer: B


The answer is B and it's simple. But I want to give a detailed explanation of this so that other similar problems can be tackled. So here we go.

1st of all this is neither a Geometric nor Arithmetic Sequence so we can't use any of those tricks here. We have to build it using the basic concept of defining Sequences.
If we think of it in an inductive way :
We have to think about it in a bottom-up manner. We have to think about it in terms of the 1st term and start building up to the bottom until we reach F11.

F3=F1+F2
F4=F2+F3
F5=F3+F4
....
F11 = F9+F10

If we think of it in a deductive way:
We have to think in a top-down manner. Breaking the actual problem into previous terms. So we start with F11 right away.
F11 =F9+F10
= {(F7+F8)+(F8+F9)}
= .........until we reach the base case.

In either case, the formula is simple as I have shown.



I don't agree since the pattern does not suggest the sequence is as we see it. I just had a similar problem.


"I did the same mistake assuming I've gotten the pattern but the answer was very revealing:

The reason is that there's no way that we can definitively determine ONE (and ONLY ONE) pattern in a given sequence.

Consider this example: 1, 2, 4, __
What's the missing term here?
Well, if we read the sequence as doubling from one term to the next, the next term is 8
HOWEVER, if we notice that we keep adding successively larger integers to each term (i.e., add 1, then add 2, then add 3, etc.) the next term is 7

Likewise, (if we want to get a bit silly), we might look at the given sequence (5, 10, 15, 20, 25, __) and say that the next term is 88. Why?
Because 5 is my favorite number, 10 is my 2nd favorite number, 15 is my 3rd favorite number, ... and 88 is 6th favorite number.

So, although you might have found a certain pattern in the sequence (double and add 1), we can't be certain that this is THE pattern.
This means t_5 can have ANY numeric value."
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Shivin
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Re: 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . [#permalink] New post   21 Oct 2025, 05:05
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Hello Carcass, I just saw a similar question which says that the sequence needs to be explicitly defined and there's no way that we can definitively determine one pattern. Hence the answer was D. Could you please elaborate on this:

https://gre.myprepclub.com/forum/in-seq ... ml#p131198

I did spot the pattern in the above question, but was not sure if I should go with it. What should be included in the question stem for us to go ahead with the spotted pattern. Please help, thanks a lot
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Carcass
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1, 1, 2, 3, 5, 8, 13, 21, 34, . . . [#permalink] New post   21 Oct 2025, 09:06
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Sir it depends on the question.

usually the rule for the sequence must be explicitly stated. Hoqwever, even on the GMAT sometimes we should be infer it

In the question by Brent, the sequence is stated.

Attachment:
Screenshot 2025-10-21 190508.png
Screenshot 2025-10-21 190508.png [ 10.27 KiB | Viewed 2470 times ]


And even in this question we are discussing is stated

1+1=2

2+3=5

5+3=8

8+5=13

The term you have + the previous one
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pihu25
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Re: 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . [#permalink] New post   15 May 2026, 09:36
I am a bit confused. Do we have to infer the series or go by the cardinal rules:

1) first term or last term should be given
2) common difference must be given
3) number of terms must be given (optional cuz an infinite sequence is also a sequence)
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Re: 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . [#permalink] New post   15 May 2026, 14:59
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We already told that sir.

Usually on the GRE how to calculate the sequence is given
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Re: 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . [#permalink]
15 May 2026, 14:59
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