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Sequences

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by dtweah » Thu May 28, 2009 5:38 am
In a sequence, the first three values are the first three positive prime integers in ascending order, and each of the successive values is the sum of all of the preceding values. What is the ratio of the 30th term to the 25th term?

A. 4/3

B.10/3

C. 20/3

D. 32/1

E. 64/1
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by mikeCoolBoy » Thu May 28, 2009 5:56 am
IMO D.

The values of the sequence are 2,3,5,10,20,40,80 ....
If we look at the pattern we can tell that for n > 3 all the numbers have 2 and 5 as factors

S4 = 10 = 2 x 5
S5 = 20 = 2^2 x 5
S6 = 40 = 2^3 x 5

Sn = 2^(n-3) x 5

The 30th term is 2 ^(27) x 5 and the 25th is 2 ^(22) x 5; therefore the ratio is 2 ^(27) x 5 / 2 ^(22) x 5 = 2 ^ 5 = 32
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by abhinav85 » Thu May 28, 2009 6:32 am
Hey mikecoolboy

Nice logic man but how did you made this formula???

Sn = 2^(n-3) x 5??

can you explain this?
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by mikeCoolBoy » Thu May 28, 2009 8:05 am
Sure you just have to take a look at the terms of the sequence. As I wrote.

S4 = 2 x 5
S5 = 2 ^ 2 x 5
S6 = 2 ^ 3 x 5

so Sn = 2 ^(y) x 5 and we have to calculate y according to n.
When n = 4 y = 1
when n = 5 y =2
so you can see that n - y = 3 and therefore y = n -3

I'm really bad at explaining things, maybe someone has another solution more clear.
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by cata1yst » Thu May 28, 2009 8:26 am
I chose D as well...

I solved it like this...

I knew the sequence up the 10th value was:

2, 3, 5, 10, 20, 40, 80, 160, 320, 640...

The ratio for the sequence is going to stay the same thoughout between n and n+5 for n >= 3.

SO

I just selected to find the ratio between the 10th integer and the 5th.

With that you get 640/20, which equals 32/1.
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by dumb.doofus » Thu May 28, 2009 10:25 am
cata1yst wrote:I chose D as well...

I solved it like this...

I knew the sequence up the 10th value was:

2, 3, 5, 10, 20, 40, 80, 160, 320, 640...

The ratio for the sequence is going to stay the same thoughout between n and n+5 for n >= 3.

SO

I just selected to find the ratio between the 10th integer and the 5th.

With that you get 640/20, which equals 32/1.
Brilliant man!!! nice logic..
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