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 March 22nd, 2014, 11:56 PM #1 Senior Member   Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 Geometric progression. Given a geometric progression 10,8,6.4,...., find the sum from the 3rd term to the 7th term of the geometric progression. Why I can't get the answer 10? Can someone show me the solution?
 March 23rd, 2014, 02:39 AM #2 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 Re: Geometric progression. You can use a formula , http://en.m.wikipedia.org/wiki/Geometric_progression Using the formula in the link above for a geometric sum you would find the sum of the first 7 terms then subtract the sum of the first 2 terms. I will do it the old fashioned (fun) way. The constant ratio is $\frac{8}{10} \= \ \frac{4}{5}$ Write down the 3rd to 7th terms $6.4 \ , \ 6.4 \cdot $$\frac{4}{5}$$ \ , \ 6.4 \cdot $$\frac{4}{5}$$^2 \ , \ 6.4 \cdot $$\frac{4}{5}$$^3 \ , \ 6.4 \cdot $$\frac{4}{5}$$^4$ Now add them up $6.4 $$1 \ + \ \frac{4}{5} \ + \ \frac{16}{25} \ + \ \frac{64}{125} \ + \ \frac{256}{625}$$ \=$ $6.4 $$\frac{625 \ + \ 4(125) \ + \ 16(25) \ + \ 64(5) \ + \ 256 }{625}$$ \=$ $\frac{32}{5} $$\frac{2101}{625}$$$ This does not reduce because there are no factors of 5 in niether 32 nor 2101 AND there are no factors of 2 in niether 5 nor 625. You can get a decimal approximation if you wish. Let us know if you have any questions about this or the wiki link referenced.
March 23rd, 2014, 04:50 AM   #3
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Re: Geometric progression.

Quote:
 Originally Posted by jiasyuen Given a geometric progression 10,8,6.4,...., find the sum from the 3rd term to the 7th term of the geometric progression. Why I can't get the answer 10? Can someone show me the solution?
As agentredlum pointed out $\frac{8}{10}= \frac{4}{5}$.

That is "6.4" not "6,4" isn't it? With my bad vision, I thought that was an arithmetic progression! Yes, $\frac{6.4}{8}= \frac{4}{5}$ so it is the beginning of a geometric progression!

March 23rd, 2014, 11:35 AM   #4
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Re: Geometric progression.

Quote:
 Originally Posted by jiasyuen Given a geometric progression 10,8,6.4,....,
Is that correct, or should it be 10,8,6,4? If so, it's arithmetic, not geometric...

 March 23rd, 2014, 02:24 PM #5 Math Team   Joined: Apr 2010 Posts: 2,780 Thanks: 361 Re: Geometric progression. In the Netherlands, among other countries, a comma (,) is used as a decimal mark. Though I've merely gotten used to use a point to, which sometimes leads to comments about it on Dutch boards.
March 23rd, 2014, 05:23 PM   #6
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Re: Geometric progression.

Quote:
 Originally Posted by jiasyuen Given a geometric progression 10,8,6.4,...., find the sum from the 3rd term to the 7th term of the geometric progression. Why I can't get the answer 10? Can someone show me the solution?
IF you're saying that 10 IS the given answer, then (as I pointed out earlier)
your 6.4 should be 6,4 (3rd and 4th terms) and the progression is ARITHMETIC;
6 + 4 + 2 + 0 - 2 = 10
Use google to find the formula...

March 23rd, 2014, 05:33 PM   #7
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Re: Geometric progression.

Quote:
Originally Posted by Denis
Quote:
 Originally Posted by jiasyuen Given a geometric progression 10,8,6.4,...., find the sum from the 3rd term to the 7th term of the geometric progression. Why I can't get the answer 10? Can someone show me the solution?
IF you're saying that 10 IS the given answer, then (as I pointed out earlier)
your 6.4 should be 6,4 (3rd and 4th terms) and the progression is ARITHMETIC;
6 + 4 + 2 + 0 - 2 = 10
Use google to find the formula...
No wonder I can't find the answer. I think my teacher has given me a wrong question. Thanks guys.

 March 23rd, 2014, 08:29 PM #8 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,414 Thanks: 1024 Re: Geometric progression. Well, if you're dealing with arithmetic series, and you want to calculate the sum of the last m terms: n = number of terms a = 1st term d = difference Sum last m terms = n/2[2a + d(n-1)] - (m-1)/2[2a + d(m-2)] Example: 2,5,8,11,14,17,20 : sum of last 4 ? a = 2 d = 3 n = 7 m = 4 Sum last 4 = 7/2[2(2) + 3(7-1) - (4-1)/2[2(2) + 3(4-2)] = 62 ; 11+14+17+20 = 62 Got that?

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### Geometric progression 1st is 7 and 4th is 56 then 7th term is

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