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the sum of the 41st and 42nd terms of the sequence
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07 Sep 2022, 00:11
07 Sep 2022, 00:11
1
Expert Reply
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Question Stats:
57% (00:54) correct
42% (00:44) wrong based on 26 sessions
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1, 1, 2, 3, 5, 8, 13, 21, 34, . . .
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
Quantity A |
Quantity B |
the sum of the 41st and 42nd terms of the sequence |
the 43rd term of the sequence |
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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the sum of the 41st and 42nd terms of the sequence
[#permalink]
07 Sep 2022, 01:26
07 Sep 2022, 01:26
1
The answer is C 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 F43.
F3=F1+F2
F4=F2+F3
F5=F3+F4
....
F43 = F41+F42
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 F43 right away.
F43 =F41+F42
= {(F40+F39)+(F41+F40)}
= .........until we reach the base case.
In either case, the formula is simple as I have shown.
As we can clearly see that both are equal. Thus the Answer is C.
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 F43.
F3=F1+F2
F4=F2+F3
F5=F3+F4
....
F43 = F41+F42
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 F43 right away.
F43 =F41+F42
= {(F40+F39)+(F41+F40)}
= .........until we reach the base case.
In either case, the formula is simple as I have shown.
As we can clearly see that both are equal. Thus the Answer is C.
Re: the sum of the 41st and 42nd terms of the sequence
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24 Jan 2025, 13:01
24 Jan 2025, 13:01
GreenlightTestPrep would this actually be true based on the explanation and problems you have for other sequences?
forum/in-sequence-x-term-1-3-term-2-7-term-29588.html#p97013 as an example
forum/in-sequence-x-term-1-3-term-2-7-term-29588.html#p97013 as an example
