The sequence a1, a2 ,a3...,an of n integers is such that ak=k if k is odd and ak=-(ak-1) if k is even. Is the sum of the terms in the sequence positive?
A-- n is odd.
B-- an is positive..
The answer is D.-Gmat Prep
Could someone provide me with an explanation as to how I can go about solving this problem. Thanks....
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- Guest
(1) n is odd
If n is 5, for instance, then a5=5, a4=-3, a3=3, a2=-1, a1=1 (I used each of the equations listed above to get these numbers I just followed the pattern) When added together [5+(-3)+(3)+(-1)+(1)] the result is +ve5
You could also plug-in 7 for n to make sure and you would still get a +ve result-follow the same pattern.
This statement alone is sufficient.
(2) an is +ve/ means the result must be +ve not zero or -ve
If n=5 (you get the same result as in statement 1)
However, if you let n=4/ following the same procedure as above (statement 1) you will see that the result is 0; therefore, one can conclude that n must be an odd number to get a +ve result. n cannot be even. This statement alone is also sufficient.
The answer is D.
If n is 5, for instance, then a5=5, a4=-3, a3=3, a2=-1, a1=1 (I used each of the equations listed above to get these numbers I just followed the pattern) When added together [5+(-3)+(3)+(-1)+(1)] the result is +ve5
You could also plug-in 7 for n to make sure and you would still get a +ve result-follow the same pattern.
This statement alone is sufficient.
(2) an is +ve/ means the result must be +ve not zero or -ve
If n=5 (you get the same result as in statement 1)
However, if you let n=4/ following the same procedure as above (statement 1) you will see that the result is 0; therefore, one can conclude that n must be an odd number to get a +ve result. n cannot be even. This statement alone is also sufficient.
The answer is D.
- Guest
Additional info: For Clarification
Additional Note:
If n is 5 I used the first 5 numbers that is, 1,2,3,4,5 and plugged them back into the equation and followed the pattern. I did the same for 4 I used 1,2,3,4. This is how I solved this problem.
If n is 5 I used the first 5 numbers that is, 1,2,3,4,5 and plugged them back into the equation and followed the pattern. I did the same for 4 I used 1,2,3,4. This is how I solved this problem.
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
ok, when you have a problem like this one - featuring an absolutely crazy-looking formula - you should immediately start writing out terms of the sequence, and going for the good old fashioned pattern recognition angle.
if you just follow the formula, you arrive at
a1 = 1
a2 = -1
a3 = 3
a4 = -3
a5 = 5
etc
the pattern is pretty obvious.
and the SUMS of the terms are**
sum1 = 1
sum2 = 0
sum3 = 3
sum4 = 0
sum5 = 5
etc
this pattern is also pretty obvious (it's n if n is odd, and 0 if n is even).
based on this pattern recognition, we can realize that the question can be rephrased as, is n odd?
--
statement (1)
sufficient
statement (2)
notice that the positive terms are exactly those for which n is odd, so this statement is basically telling us that n is odd.
sufficient
ans = d
--
**note that we bother to find these only because the problem specifically asks about them. you wouldn't want to spend the time to find them if you didn't have a reason to do so.
if you just follow the formula, you arrive at
a1 = 1
a2 = -1
a3 = 3
a4 = -3
a5 = 5
etc
the pattern is pretty obvious.
and the SUMS of the terms are**
sum1 = 1
sum2 = 0
sum3 = 3
sum4 = 0
sum5 = 5
etc
this pattern is also pretty obvious (it's n if n is odd, and 0 if n is even).
based on this pattern recognition, we can realize that the question can be rephrased as, is n odd?
--
statement (1)
sufficient
statement (2)
notice that the positive terms are exactly those for which n is odd, so this statement is basically telling us that n is odd.
sufficient
ans = d
--
**note that we bother to find these only because the problem specifically asks about them. you wouldn't want to spend the time to find them if you didn't have a reason to do so.
- bish
- Forum Guests
- Posts: 13
- Joined: Sun Jul 29, 2012 10:22 am
Re: The sequence a1, a2 ,a3...,an of n integers is such that a[s
Hi Ron,
Why don't we take negative possibilities of a_n into cosideration in the problem,
For example the answer changes if say n = -5 .
Why don't we take negative possibilities of a_n into cosideration in the problem,
For example the answer changes if say n = -5 .
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
Re: The sequence a1, a2 ,a3...,an of n integers is such that a[s
bish Wrote:Hi Ron,
Why don't we take negative possibilities of a_n into cosideration in the problem,
For example the answer changes if say n = -5 .
the first few words of the problem are "The sequence a1, a2, a3, ...", thus implying that the sequence starts with n = 1.
--
more generally, you will never, ever, ever see something like "the -5th term of a sequence". because that's just not something that really happens.
there's a slim off-chance that you might have to contend with "a_0", but there is no way that you'll ever have a_n for negative values of n. it's just not a thing.
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