Me possibly overthinking a geometric series question












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I am creating a study sheet for geometric series and came across this questions




Do you think there is an infinite geometric series with first term 10 and a sum of 4? If so, find one infinite geometric series with first term 10 and a sum of 4, as well as explain how you get this infinite geometric series. If not, explain why.




This is possible with some neagitve common ratio, r, where $|r|<1$ correct?










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  • $begingroup$
    What have you tried so far? What $r$ do you have in mind?
    $endgroup$
    – platty
    Dec 4 '18 at 0:33
















0












$begingroup$


I am creating a study sheet for geometric series and came across this questions




Do you think there is an infinite geometric series with first term 10 and a sum of 4? If so, find one infinite geometric series with first term 10 and a sum of 4, as well as explain how you get this infinite geometric series. If not, explain why.




This is possible with some neagitve common ratio, r, where $|r|<1$ correct?










share|cite|improve this question









$endgroup$












  • $begingroup$
    What have you tried so far? What $r$ do you have in mind?
    $endgroup$
    – platty
    Dec 4 '18 at 0:33














0












0








0





$begingroup$


I am creating a study sheet for geometric series and came across this questions




Do you think there is an infinite geometric series with first term 10 and a sum of 4? If so, find one infinite geometric series with first term 10 and a sum of 4, as well as explain how you get this infinite geometric series. If not, explain why.




This is possible with some neagitve common ratio, r, where $|r|<1$ correct?










share|cite|improve this question









$endgroup$




I am creating a study sheet for geometric series and came across this questions




Do you think there is an infinite geometric series with first term 10 and a sum of 4? If so, find one infinite geometric series with first term 10 and a sum of 4, as well as explain how you get this infinite geometric series. If not, explain why.




This is possible with some neagitve common ratio, r, where $|r|<1$ correct?







geometric-series






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share|cite|improve this question











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asked Dec 4 '18 at 0:31









K MathK Math

60039




60039












  • $begingroup$
    What have you tried so far? What $r$ do you have in mind?
    $endgroup$
    – platty
    Dec 4 '18 at 0:33


















  • $begingroup$
    What have you tried so far? What $r$ do you have in mind?
    $endgroup$
    – platty
    Dec 4 '18 at 0:33
















$begingroup$
What have you tried so far? What $r$ do you have in mind?
$endgroup$
– platty
Dec 4 '18 at 0:33




$begingroup$
What have you tried so far? What $r$ do you have in mind?
$endgroup$
– platty
Dec 4 '18 at 0:33










1 Answer
1






active

oldest

votes


















3












$begingroup$

You know that if $a$ is the first term of a geometric series and $r$ is the ratio, then the sum is given by
$$S=sum_{n=0}^infty ar^n=frac{a}{1-r}$$
So, if $a=10$ and $S=4$, then
$$frac{10}{1-r}=4implies r=-frac{3}{2}$$
but the series does not converge in this case, so the solution is extraneous and the described situation is not possible.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
    $endgroup$
    – K Math
    Dec 4 '18 at 0:43











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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









3












$begingroup$

You know that if $a$ is the first term of a geometric series and $r$ is the ratio, then the sum is given by
$$S=sum_{n=0}^infty ar^n=frac{a}{1-r}$$
So, if $a=10$ and $S=4$, then
$$frac{10}{1-r}=4implies r=-frac{3}{2}$$
but the series does not converge in this case, so the solution is extraneous and the described situation is not possible.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
    $endgroup$
    – K Math
    Dec 4 '18 at 0:43
















3












$begingroup$

You know that if $a$ is the first term of a geometric series and $r$ is the ratio, then the sum is given by
$$S=sum_{n=0}^infty ar^n=frac{a}{1-r}$$
So, if $a=10$ and $S=4$, then
$$frac{10}{1-r}=4implies r=-frac{3}{2}$$
but the series does not converge in this case, so the solution is extraneous and the described situation is not possible.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
    $endgroup$
    – K Math
    Dec 4 '18 at 0:43














3












3








3





$begingroup$

You know that if $a$ is the first term of a geometric series and $r$ is the ratio, then the sum is given by
$$S=sum_{n=0}^infty ar^n=frac{a}{1-r}$$
So, if $a=10$ and $S=4$, then
$$frac{10}{1-r}=4implies r=-frac{3}{2}$$
but the series does not converge in this case, so the solution is extraneous and the described situation is not possible.






share|cite|improve this answer









$endgroup$



You know that if $a$ is the first term of a geometric series and $r$ is the ratio, then the sum is given by
$$S=sum_{n=0}^infty ar^n=frac{a}{1-r}$$
So, if $a=10$ and $S=4$, then
$$frac{10}{1-r}=4implies r=-frac{3}{2}$$
but the series does not converge in this case, so the solution is extraneous and the described situation is not possible.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 4 '18 at 0:34









FrpzzdFrpzzd

22.5k840108




22.5k840108












  • $begingroup$
    ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
    $endgroup$
    – K Math
    Dec 4 '18 at 0:43


















  • $begingroup$
    ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
    $endgroup$
    – K Math
    Dec 4 '18 at 0:43
















$begingroup$
ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
$endgroup$
– K Math
Dec 4 '18 at 0:43




$begingroup$
ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
$endgroup$
– K Math
Dec 4 '18 at 0:43


















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