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exponenet fun!!

by vinviper1 » Thu Mar 27, 2008 8:06 pm
What is the sum of the 20th and 21st terms in the sequence 1, 3, 9, 27... where each term is 3 times the preceding term?

1. 4×3*19
2. 10×3*19
3. 4×3*20
4. 10×3*20
5. 339


1

Thanks!
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by camitava » Thu Mar 27, 2008 8:15 pm
This is a GP. To find nth term in GP, the formula is = a * r^(n - 1) where a = first term and r = common ratio. Here a = 1 and r = 3.
So 20th term = 1 * 3^19 = 3^19
So 21st term = 1 * 3^20 = 3^20
Add this two : 3^19(1 + 3) = 3^19 * 4 - So option 1 is the best one to chose!
Correct me If I am wrong


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by Kaunteya1 » Fri Mar 28, 2008 1:18 pm
Amitava is correct.

1, 3, 9, 27, 81... = 3^0, 3^1, 3^2... The 1st term is 3^0 so the 20th term is 3^19 and the 21st term is 3^20.

3^19 + 3^20 =

3^19(1) + 3^19(3) from step one, basically 3^20 is the same a 3x3x3...(until you have twenty 3's multiplyed together) or 3^20 can be rewritten at 3^19(3) or 3^18(3x3) or 3^17(3x3x3) ect...

So now factor out 3^19 from both 3^19(1) and 3^19(3) this give you
3^19(1 + 3). Just multiply 3^19 back into the () and you get the orignal 3^19 + 3^20.

Finally just add 1+3=4 and then the original 3^19 + 3^20 equals 3^19(4) or A.
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ok

by resilient » Mon Mar 31, 2008 1:18 am
ok so far my approach has been the same but a tad different.

I established the 1 2 9 27 81 243 729 2167 (notice the pattern in units digit.

so the units digitn in th e20th number will end in 7 and 21st number will end in 1 with a units digit of 8 in the final number. Now I just dont understand what the asterik stands for. DOes this mean a secondary multiplication? I hope my approach is right?


please let me know!
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Re: ok

by camitava » Mon Mar 31, 2008 2:12 am
Enginpasa1 wrote:ok so far my approach has been the same but a tad different.

I established the 1 2 9 27 81 243 729 2167 (notice the pattern in units digit.

so the units digitn in th e20th number will end in 7 and 21st number will end in 1 with a units digit of 8 in the final number. Now I just dont understand what the asterik stands for. DOes this mean a secondary multiplication? I hope my approach is right?


please let me know!
Enginpasa, by '*', I tried to mean multiplication. Sorry for the confusion! Look Engin, the main thing I believe is you have to answer the Qs correctly in GMAT in whatever way you follow and that's the main thing.
Correct me If I am wrong


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by vinviper1 » Mon Mar 31, 2008 10:29 am
Thanks! What do you mean by this being a GP?
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by humeixia » Thu Apr 10, 2008 2:02 pm
GP?
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by camitava » Thu Apr 10, 2008 5:43 pm
GP means Geometric Progression. Do a google search on this and u will get to know ...
Correct me If I am wrong


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I UNDERSTAND

by resilient » Fri Apr 11, 2008 8:56 am
THank you for the heads up Camitava. I have been working on that. I guess the hard part of this question is to learn how to extract the formula out of the way. Where can I learn to how to get better on this!?
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Re: I UNDERSTAND

by gabriel » Fri Apr 11, 2008 10:00 am
Enginpasa1 wrote:THank you for the heads up Camitava. I have been working on that. I guess the hard part of this question is to learn how to extract the formula out of the way. Where can I learn to how to get better on this!?
Read the basics on Progressions (a simple google search will give you enough material). Once your done with them, post your doubts on this thread I will try and answer them.
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