Geometric Progressions ratio
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I don't really know how to find the ratio of 3/2, any ideas? thanks!
discrete-mathematics
asked Dec 28 '18 at 17:08
Tom1999Tom1999
445
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add a comment |
$begingroup$
I don't really know how to find the ratio of 3/2, any ideas? thanks!
discrete-mathematics
asked Dec 28 '18 at 17:08
Tom1999Tom1999
445
$endgroup$
3
$begingroup$
The ratio for a geometric progression is nothing but $frac{a_{n+1}}{a_n}$ which is equal to 3/2.
$endgroup$
– toric_actions
Dec 28 '18 at 17:10
4
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Just divide two consecutive terms ($n^{th}$ by $(n-1)^{th}$) to see what the ratio is: $$frac{3^3cdot 2^{16}}{3^2cdot2^{17}} = frac{3}{2}$$
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– KM101
Dec 28 '18 at 17:10
1
$begingroup$
It would really help if you would put this in context, explain what the text is attempting to demonstrate, and just what the question is. The ratio of what exact. The ratio of $frac 32$ is just $frac 32$ and the ratio $frac {14}{27}$ is $frac {14}{27}$. So asking what the ratio doesn't mean anything. In this case you are asked for the ratio between consecutive terms of a geometric series so it'd be useful if you said that. In which case you just divide two terms: $frac {3^32^{16}}{3^22^{17}} = frac 32$.
$endgroup$
– fleablood
Dec 28 '18 at 17:40
add a comment |
$begingroup$
I don't really know how to find the ratio of 3/2, any ideas? thanks!
discrete-mathematics
asked Dec 28 '18 at 17:08
Tom1999Tom1999
445
$endgroup$
I don't really know how to find the ratio of 3/2, any ideas? thanks!
discrete-mathematics
discrete-mathematics
asked Dec 28 '18 at 17:08
Tom1999Tom1999
445
asked Dec 28 '18 at 17:08
Tom1999Tom1999
445
asked Dec 28 '18 at 17:08
Tom1999Tom1999
445
asked Dec 28 '18 at 17:08
Tom1999Tom1999
445
asked Dec 28 '18 at 17:08
Tom1999Tom1999
445
445
3
$begingroup$
The ratio for a geometric progression is nothing but $frac{a_{n+1}}{a_n}$ which is equal to 3/2.
$endgroup$
– toric_actions
Dec 28 '18 at 17:10
4
$begingroup$
Just divide two consecutive terms ($n^{th}$ by $(n-1)^{th}$) to see what the ratio is: $$frac{3^3cdot 2^{16}}{3^2cdot2^{17}} = frac{3}{2}$$
$endgroup$
– KM101
Dec 28 '18 at 17:10
1
$begingroup$
It would really help if you would put this in context, explain what the text is attempting to demonstrate, and just what the question is. The ratio of what exact. The ratio of $frac 32$ is just $frac 32$ and the ratio $frac {14}{27}$ is $frac {14}{27}$. So asking what the ratio doesn't mean anything. In this case you are asked for the ratio between consecutive terms of a geometric series so it'd be useful if you said that. In which case you just divide two terms: $frac {3^32^{16}}{3^22^{17}} = frac 32$.
$endgroup$
– fleablood
Dec 28 '18 at 17:40
add a comment |
3
$begingroup$
The ratio for a geometric progression is nothing but $frac{a_{n+1}}{a_n}$ which is equal to 3/2.
$endgroup$
– toric_actions
Dec 28 '18 at 17:10
4
$begingroup$
Just divide two consecutive terms ($n^{th}$ by $(n-1)^{th}$) to see what the ratio is: $$frac{3^3cdot 2^{16}}{3^2cdot2^{17}} = frac{3}{2}$$
$endgroup$
– KM101
Dec 28 '18 at 17:10
1
$begingroup$
It would really help if you would put this in context, explain what the text is attempting to demonstrate, and just what the question is. The ratio of what exact. The ratio of $frac 32$ is just $frac 32$ and the ratio $frac {14}{27}$ is $frac {14}{27}$. So asking what the ratio doesn't mean anything. In this case you are asked for the ratio between consecutive terms of a geometric series so it'd be useful if you said that. In which case you just divide two terms: $frac {3^32^{16}}{3^22^{17}} = frac 32$.
$endgroup$
– fleablood
Dec 28 '18 at 17:40
3
3
$begingroup$
The ratio for a geometric progression is nothing but $frac{a_{n+1}}{a_n}$ which is equal to 3/2.
$endgroup$
– toric_actions
Dec 28 '18 at 17:10
$begingroup$
The ratio for a geometric progression is nothing but $frac{a_{n+1}}{a_n}$ which is equal to 3/2.
$endgroup$
– toric_actions
Dec 28 '18 at 17:10
4
4
$begingroup$
Just divide two consecutive terms ($n^{th}$ by $(n-1)^{th}$) to see what the ratio is: $$frac{3^3cdot 2^{16}}{3^2cdot2^{17}} = frac{3}{2}$$
$endgroup$
– KM101
Dec 28 '18 at 17:10
$begingroup$
Just divide two consecutive terms ($n^{th}$ by $(n-1)^{th}$) to see what the ratio is: $$frac{3^3cdot 2^{16}}{3^2cdot2^{17}} = frac{3}{2}$$
$endgroup$
– KM101
Dec 28 '18 at 17:10
1
1
$begingroup$
It would really help if you would put this in context, explain what the text is attempting to demonstrate, and just what the question is. The ratio of what exact. The ratio of $frac 32$ is just $frac 32$ and the ratio $frac {14}{27}$ is $frac {14}{27}$. So asking what the ratio doesn't mean anything. In this case you are asked for the ratio between consecutive terms of a geometric series so it'd be useful if you said that. In which case you just divide two terms: $frac {3^32^{16}}{3^22^{17}} = frac 32$.
$endgroup$
– fleablood
Dec 28 '18 at 17:40
$begingroup$
It would really help if you would put this in context, explain what the text is attempting to demonstrate, and just what the question is. The ratio of what exact. The ratio of $frac 32$ is just $frac 32$ and the ratio $frac {14}{27}$ is $frac {14}{27}$. So asking what the ratio doesn't mean anything. In this case you are asked for the ratio between consecutive terms of a geometric series so it'd be useful if you said that. In which case you just divide two terms: $frac {3^32^{16}}{3^22^{17}} = frac 32$.
$endgroup$
– fleablood
Dec 28 '18 at 17:40
add a comment |
1 Answer
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$begingroup$
Simply notice that each successive term is tripled the previous ($times 3$) and then halved ($times 1/2$). It's more a pattern-recognition thing than anything formal.
Of course, if you want, you can manually divide any $n^{th}$ term by the preceding term to also see the ratio in a geometric series. That would be the more proper way to demonstrate that the ratio of the series is $3/2$.
answered Dec 28 '18 at 17:12
Eevee TrainerEevee Trainer
8,24521439
$endgroup$
$begingroup$
Thank you guys! I got it!
$endgroup$
– Tom1999
Dec 28 '18 at 20:00
add a comment |
Your Answer
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$begingroup$
Simply notice that each successive term is tripled the previous ($times 3$) and then halved ($times 1/2$). It's more a pattern-recognition thing than anything formal.
Of course, if you want, you can manually divide any $n^{th}$ term by the preceding term to also see the ratio in a geometric series. That would be the more proper way to demonstrate that the ratio of the series is $3/2$.
answered Dec 28 '18 at 17:12
Eevee TrainerEevee Trainer
8,24521439
$endgroup$
$begingroup$
Thank you guys! I got it!
$endgroup$
– Tom1999
Dec 28 '18 at 20:00
add a comment |
$begingroup$
Simply notice that each successive term is tripled the previous ($times 3$) and then halved ($times 1/2$). It's more a pattern-recognition thing than anything formal.
Of course, if you want, you can manually divide any $n^{th}$ term by the preceding term to also see the ratio in a geometric series. That would be the more proper way to demonstrate that the ratio of the series is $3/2$.
answered Dec 28 '18 at 17:12
Eevee TrainerEevee Trainer
8,24521439
$endgroup$
$begingroup$
Thank you guys! I got it!
$endgroup$
– Tom1999
Dec 28 '18 at 20:00
add a comment |
$begingroup$
Simply notice that each successive term is tripled the previous ($times 3$) and then halved ($times 1/2$). It's more a pattern-recognition thing than anything formal.
Of course, if you want, you can manually divide any $n^{th}$ term by the preceding term to also see the ratio in a geometric series. That would be the more proper way to demonstrate that the ratio of the series is $3/2$.
answered Dec 28 '18 at 17:12
Eevee TrainerEevee Trainer
8,24521439
$endgroup$
Simply notice that each successive term is tripled the previous ($times 3$) and then halved ($times 1/2$). It's more a pattern-recognition thing than anything formal.
Of course, if you want, you can manually divide any $n^{th}$ term by the preceding term to also see the ratio in a geometric series. That would be the more proper way to demonstrate that the ratio of the series is $3/2$.
answered Dec 28 '18 at 17:12
Eevee TrainerEevee Trainer
8,24521439
answered Dec 28 '18 at 17:12
Eevee TrainerEevee Trainer
8,24521439
answered Dec 28 '18 at 17:12
Eevee TrainerEevee Trainer
8,24521439
answered Dec 28 '18 at 17:12
Eevee TrainerEevee Trainer
8,24521439
8,24521439
$begingroup$
Thank you guys! I got it!
$endgroup$
– Tom1999
Dec 28 '18 at 20:00
add a comment |
$begingroup$
Thank you guys! I got it!
$endgroup$
– Tom1999
Dec 28 '18 at 20:00
$begingroup$
Thank you guys! I got it!
$endgroup$
– Tom1999
Dec 28 '18 at 20:00
$begingroup$
Thank you guys! I got it!
$endgroup$
– Tom1999
Dec 28 '18 at 20:00
add a comment |
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3
$begingroup$
The ratio for a geometric progression is nothing but $frac{a_{n+1}}{a_n}$ which is equal to 3/2.
$endgroup$
– toric_actions
Dec 28 '18 at 17:10
4
$begingroup$
Just divide two consecutive terms ($n^{th}$ by $(n-1)^{th}$) to see what the ratio is: $$frac{3^3cdot 2^{16}}{3^2cdot2^{17}} = frac{3}{2}$$
$endgroup$
– KM101
Dec 28 '18 at 17:10
1
$begingroup$
It would really help if you would put this in context, explain what the text is attempting to demonstrate, and just what the question is. The ratio of what exact. The ratio of $frac 32$ is just $frac 32$ and the ratio $frac {14}{27}$ is $frac {14}{27}$. So asking what the ratio doesn't mean anything. In this case you are asked for the ratio between consecutive terms of a geometric series so it'd be useful if you said that. In which case you just divide two terms: $frac {3^32^{16}}{3^22^{17}} = frac 32$.
$endgroup$
– fleablood
Dec 28 '18 at 17:40