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In a sequence k, each term after the second term is the sum  [#permalink]

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In a sequence k, each term after the second term is the sum of the two previous terms. What is the first term of sequence K?

(1) one term of sequence K is 29
(2) The 4th and 5th terms of K are 11 and 18, respectively

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Re: In a sequence k, each term after the second term is the sum  [#permalink]

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MensaNumber wrote:
In a sequence k, each term after the second term is the sum of the two previous terms. What is the first term of sequence K?

1)one term of sequence K is 29
2)The 4th and 5th terms of K are 11 and 18, respectively

Dear MensaNumber,
I'm happy to help. Incidentally, a sequence following this pattern is known as a Fibonacci sequence. The most famous one, {1, 1, 2, 3, 5, etc.} has deep connections to the Golden Ratio and to many structures in Nature. See:
http://www.goldennumber.net/category/math/

In this problem is another Fibonacci sequence.

Statement #1: if we know one term is 29, then it may be that this is the third term, after 14 and 15, or 1 and 28, or -2 and 31, or etc. Or, it may be a later term, the fourth or fifth or sixth, in which case the first term could be almost anything. On the basis of this piece of information, we know nothing.

Statement #2: a4 = 11 and a5 = 18.
We know a3 + a4 = a5, so a3 + 11 = 18, and a3 = 7
Then, we know a2 + a3 = a4, so a2 + 7 = 11, and a2 = 4
Then, we know a1 + a2 = a3, so a1 + 4 = 7, so a1 = 3
This statement, alone and by itself, is sufficient for answering the prompt question.

Does all this make sense?
Mike _________________
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Re: In a sequence k, each term after the second term is the sum  [#permalink]

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MensaNumber wrote:
In a sequence k, each term after the second term is the sum of the two previous terms. What is the first term of sequence K?

1)one term of sequence K is 29
2)The 4th and 5th terms of K are 11 and 18, respectively

Sequene k: a; b; a + b; a+2b; 2a + 3b

(1) one term of sequence K is 29, For example: 2a+3b = 29, there is many solution for a and b ---> insufficient
(2) a + 2b = 11 and 2a + 3b = 18 ---> a = 7 ---> sufficient
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In a sequence k, each term after the second term is the sum  [#permalink]

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Are we supposed to ignore negative numbers when dealing with sequence problems? For example, I wrote out the numbers of statement 2 and found it to be insufficient ~ 3, -1, 2, 1, 3, 4, 7, 11, 18 (going backwards to negative infiniti) Am i overthinking it?
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Re: In a sequence k, each term after the second term is the sum  [#permalink]

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I think this is a poor quality question and the explanation is not clear enough.
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In a sequence k, each term after the second term is the sum  [#permalink]

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wmichaelxie wrote:
Are we supposed to ignore negative numbers when dealing with sequence problems? For example, I wrote out the numbers of statement 2 and found it to be insufficient ~ 3, -1, 2, 1, 3, 4, 7, 11, 18 (going backwards to negative infiniti) Am i overthinking it?

wmichaelxie wrote:
I think this is a poor quality question and the explanation is not clear enough.

I must say you are overthinking this. This is an easy question and much clear on everything.

We are given that 4th term is 11 and 5th term is 18. So, in the sequence you have mentioned above, I couldn't see your statement 2 is matching. So, its an incorrect sequence.

If I take a sequence as a, b, a + b, a + 2b, 2a + 3b ,.. so on.

I will get a + 2b = 11 and 2a + 3b = 18.

On solving these equations, we will get a = 3.

Hence, B is sufficient.
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Re: In a sequence k, each term after the second term is the sum  [#permalink]

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abhimahna wrote:
wmichaelxie wrote:
Are we supposed to ignore negative numbers when dealing with sequence problems? For example, I wrote out the numbers of statement 2 and found it to be insufficient ~ 3, -1, 2, 1, 3, 4, 7, 11, 18 (going backwards to negative infiniti) Am i overthinking it?

wmichaelxie wrote:
I think this is a poor quality question and the explanation is not clear enough.

I must say you are overthinking this. This is an easy question and much clear on everything.

We are given that 4th term is 11 and 5th term is 18. So, in the sequence you have mentioned above, I couldn't see your statement 2 is matching. So, its an incorrect sequence.

If I take a sequence as a, b, a + b, a + 2b, a + 3b ,.. so on.

I will get a + 2b = 11 and a + 3b = 18.

On solving these equations, we will get a = 3.

Hence, B is sufficient.

Dear abhimahna,

My friend, you found the correct answer, but the algebraic representations you used (a, b, a + b, a + 2b, a + 3b, ...) are not correct for a recursive series. The fifth term would be 2a + 3b. Perhaps you knew this already, because you found the correct answer.

Mike _________________
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In a sequence k, each term after the second term is the sum  [#permalink]

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mikemcgarry wrote:
abhimahna wrote:
wmichaelxie wrote:
Are we supposed to ignore negative numbers when dealing with sequence problems? For example, I wrote out the numbers of statement 2 and found it to be insufficient ~ 3, -1, 2, 1, 3, 4, 7, 11, 18 (going backwards to negative infiniti) Am i overthinking it?

wmichaelxie wrote:
I think this is a poor quality question and the explanation is not clear enough.

I must say you are overthinking this. This is an easy question and much clear on everything.

We are given that 4th term is 11 and 5th term is 18. So, in the sequence you have mentioned above, I couldn't see your statement 2 is matching. So, its an incorrect sequence.

If I take a sequence as a, b, a + b, a + 2b, a + 3b ,.. so on.

I will get a + 2b = 11 and a + 3b = 18.

On solving these equations, we will get a = 3.

Hence, B is sufficient.

Dear abhimahna,

My friend, you found the correct answer, but the algebraic representations you used (a, b, a + b, a + 2b, a + 3b, ...) are not correct for a recursive series. The fifth term would be 2a + 3b. Perhaps you knew this already, because you found the correct answer.

Mike Hey Mike ( @mikemcgarry), thanks for pointing that out. It was actually a typo error. I used the 5th term as 2a + 3b only to get to the answer.

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Re: In a sequence k, each term after the second term is the sum  [#permalink]

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Great, thank you. I missed that.
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In a sequence k, each term after the second term is the sum  [#permalink]

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Prompt analysis
An = An-1 +An-2

Superset
The answer will be a real number

Translation
In order to find the answer, we need:
1# exact value of 1st term
2# any other information to find the 1st term thruogh the equation

Statement analysis
St 1: we know the one term. But we don't know the break of that term as in what two numbers have formed 29. INSUFFICIENT
St 2: 5th term =4th term +3rd term. Therfore 3rd term = 7. Similarly 4th term = 3rd term +2nd term. Therfore 2nd term = 4 and similarly 1st term is 3. ANSWER

Option B
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Re: In a sequence k, each term after the second term is the sum  [#permalink]

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