Mathematics
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OpenStudy (howard-wolowitz):
Find a general formula for the nth term of the geometric series with:
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OpenStudy (howard-wolowitz):
\[a _{5}=1/5.......r=1/2\]
OpenStudy (howard-wolowitz):
@Michele_Laino
OpenStudy (michele_laino):
please use this formula in order to get a_1:
\[{a_5} = {a_1}{r^4}\]
OpenStudy (howard-wolowitz):
ok
OpenStudy (howard-wolowitz):
could you show me how to do these but not the answer after you do the work I will figure out the answer?
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OpenStudy (howard-wolowitz):
if no then i'll do it
OpenStudy (michele_laino):
here is your step:
\[{a_1} = \frac{{{a_5}}}{{{r^4}}} = \frac{{1/5}}{{{{\left( {1/2} \right)}^4}}} = ...?\]
OpenStudy (howard-wolowitz):
ok that would be 16/5 or 3 1/5
OpenStudy (michele_laino):
that's right!
OpenStudy (howard-wolowitz):
so its a=16
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OpenStudy (michele_laino):
now, please keep in mind that the general term a_n is given by the subsequent formula:
\[{a_n} = {a_1}{r^{n - 1}}\]
OpenStudy (howard-wolowitz):
\[a _{n}=16 \left( 1/2 \right) ^{n-1}\]
OpenStudy (michele_laino):
no, I think:
\[{a_n} = {a_1}{r^{n - 1}} = \frac{{16}}{5}\frac{1}{{{2^{n - 1}}}}\]
OpenStudy (michele_laino):
since a_1 = 16/5
OpenStudy (howard-wolowitz):
so 4
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OpenStudy (howard-wolowitz):
a =2
OpenStudy (michele_laino):
pleae your answr is:
\[{a_n} = {a_1}{r^{n - 1}} = \frac{{16}}{5}\frac{1}{{{2^{n - 1}}}}\]
OpenStudy (howard-wolowitz):
but thats not a optiion
OpenStudy (michele_laino):
I don't see your options
OpenStudy (howard-wolowitz):
well a=4 ...... a=8 ....... a=16 ...... a=2
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OpenStudy (howard-wolowitz):
all have (1/2)
OpenStudy (michele_laino):
sorry what is a?
OpenStudy (michele_laino):
and n what is?
OpenStudy (michele_laino):
please, the general term has to depend on n
OpenStudy (howard-wolowitz):
ok so its what then
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OpenStudy (michele_laino):
I think that your answer is:
\[{a_n} = \frac{{16}}{5}\frac{1}{{{2^{n - 1}}}}\]
OpenStudy (howard-wolowitz):
so its the 16 one kk gotcha thxs
OpenStudy (michele_laino):
thanks!
OpenStudy (howard-wolowitz):
Find an equivalent fraction for the repeating decimal:
OpenStudy (howard-wolowitz):
\[0.218\]
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OpenStudy (howard-wolowitz):
hmm maybe 72/330
OpenStudy (michele_laino):
please I can write this:
\[0.218 = \frac{{218}}{{1000}} = \frac{{109}}{{500}}\]
OpenStudy (howard-wolowitz):
ok well u got it because a answer was 218/1000
OpenStudy (michele_laino):
since
\[\frac{{72}}{{330}} = \frac{{24}}{{110}} = \frac{{12}}{{55}}\]
then your answer can not be a right answer
OpenStudy (howard-wolowitz):
well the choices are 72/330
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OpenStudy (howard-wolowitz):
218/1000
OpenStudy (howard-wolowitz):
7/330
OpenStudy (howard-wolowitz):
126/330
OpenStudy (howard-wolowitz):
it has to be B
OpenStudy (michele_laino):
please wait are your repeated decimal 1 and 8?
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OpenStudy (howard-wolowitz):
yes 0.218
OpenStudy (michele_laino):
ok! then your ratio is:
\[\frac{{218 - 2}}{{990}} = \frac{{216}}{{990}} = \frac{{72}}{{330}}\]
OpenStudy (howard-wolowitz):
u said 218/1000 before
OpenStudy (howard-wolowitz):
but ok
OpenStudy (michele_laino):
since I don't understood your question, sorry!
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OpenStudy (howard-wolowitz):
its ok dude i dont either i feel dumb hahhaha
OpenStudy (howard-wolowitz):
converge or diverge
OpenStudy (howard-wolowitz):
new question dude sorry