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To find the first term in the sequence

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by gmattesttaker2 » Mon Dec 23, 2013 10:39 pm
Hello,

Can you please assist with this:

In a sequence of positive integers, every
term after the second equals the sum of the
two preceding ones if the sum is odd and
one-half the sum of the two preceding terms
if the sum is even. If the fourth term in the
sequence is 7 and the fifth is 5, which is the
first term in the sequence?

(A) 14
(B) 10
(C) 4
(D) 3
(E) 2

OA: E

I tried to proceed as follows:

S5 = 5 = odd => S5 = S4 + S3 => 5 = 7 + S3 = > S3 = -2
S4 = 7 = odd => S4 = S3 + S2 => 7 = (-2) + S2 => S2 = 9
S3 = -2 = even => S3 = 1/2 ( S2 + S1 ) = 1/2 ( 9 + S1 ) => -4 = 9 + S1 => S1 = -13

However, this answer is obviously wrong. Can you please assist? Thanks a lot - Sri
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by theCodeToGMAT » Mon Dec 23, 2013 11:01 pm
To find: 1st

1th
2nd
3rd =
4th = 7
5th = 5

Since, 5th is smaller then 4th.. that means 3rd is ODD
==> (3rd + 7 ) = 5*2
3rd = 3

So,
2nd
3rd = 3
4th = 7
5th = 5

Since, 4th is ODD that means 2nd must be EVEN
==> 2nd = 7-3 = 4

So,
1st
2nd = 4
3rd = 3
4th = 7
5th = 5

Since, 3rd is ODD and less than 2nd
==> (1st + 4) = 3*2
1st = 2
[spoiler]
{E}[/spoiler]
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by gmattesttaker2 » Mon Dec 23, 2013 11:59 pm
theCodeToGMAT wrote:To find: 1st

1th
2nd
3rd =
4th = 7
5th = 5

Since, 5th is smaller then 4th.. that means 3rd is ODD
==> (3rd + 7 ) = 5*2
3rd = 3

So,
2nd
3rd = 3
4th = 7
5th = 5

Since, 4th is ODD that means 2nd must be EVEN
==> 2nd = 7-3 = 4

So,
1st
2nd = 4
3rd = 3
4th = 7
5th = 5

Since, 3rd is ODD and less than 2nd
==> (1st + 4) = 3*2
1st = 2
[spoiler]
{E}[/spoiler]
Hi Rahul,

Thanks for the reply. I was not clear with the following:

Since, 5th is smaller then 4th.. that means 3rd is ODD

I was just wondering if you can please explain this?

Thanks,
Sri
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by theCodeToGMAT » Tue Dec 24, 2013 12:16 am
Question says that all the numbers are positive..

Now, considering three terms
3rd =
4th = 7
5th = 5

We know that all terms are positive.. so it is not possible that 5th term is smaller then 4th unless 3rd + 4th results in EVEN..

So, (3rd + 4th)/2 = 5th
=> (3rd + 7) = 5*2
=> 3rd = 3

I hope it's better now
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by gmattesttaker2 » Tue Dec 24, 2013 11:21 am
theCodeToGMAT wrote:Question says that all the numbers are positive..

Now, considering three terms
3rd =
4th = 7
5th = 5

We know that all terms are positive.. so it is not possible that 5th term is smaller then 4th unless 3rd + 4th results in EVEN..

So, (3rd + 4th)/2 = 5th
=> (3rd + 7) = 5*2
=> 3rd = 3

I hope it's better now
Hello Rahul,

Thank you very much for clarifying.

Best Regards,
Sri
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