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anonymous
 one year ago
FAN/MEDAL
What is the sum of an 8term geometric series if the first term is 11, the last term is 859,375, and the common ratio is 5?
143,231
36,047
144,177
716,144
anonymous
 one year ago
FAN/MEDAL What is the sum of an 8term geometric series if the first term is 11, the last term is 859,375, and the common ratio is 5? 143,231 36,047 144,177 716,144

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amoodarya
 one year ago
Best ResponseYou've already chosen the best response.1\[S_8?\\a_1=11\\a_8=859,375\] \[s_n=a_1+a_1q+a_1q^2+...+a_1q^{n1}=\frac{a_1(1q^n)}{1q}\\s_8=a_1+a_1q+a_1q^2+...+a_1q^{7}=\frac{a_1(1q^8)}{1q}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: the sum of the first 8 terms of your geometric sequence is given by the subsequent formula: \[\Large S = {a_1}\frac{{{q^8}  1}}{{q  1}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1where q=5 and a_1= 11

amoodarya
 one year ago
Best ResponseYou've already chosen the best response.1you can write it as \[a_8=a_1q^7=11(q^7)=859,375\\q=5\] plug into formula

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1substituting your data into the formula for S, we get: \[\Large S = {a_1}\frac{{{q^8}  1}}{{q  1}} = \left( {  11} \right) \times \frac{{{{\left( {  5} \right)}^8}  1}}{{\left( {  5  1} \right)}} = ...?\] please continue

anonymous
 one year ago
Best ResponseYou've already chosen the best response.03906251 (11) 390626  x  =  = 65104.33333 x 11 = 716147.6667 6 1 6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got this wrong, right?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1please keep in mind that: \[\Large {\left( {  5} \right)^8} = 390625\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But then I added to there is a 1 in front

anonymous
 one year ago
Best ResponseYou've already chosen the best response.03906254 (11) 39062  x  =  = 65104 x 11 = 716144 6 1  6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got it is that right?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1\[{\left( {  5} \right)^8} = {\left( {  1 \times 5} \right)^8} = {\left( {  1} \right)^8}{\left( 5 \right)^8} = + {5^8} = 390625\] hint: \[S = {a_1}\frac{{{q^8}  1}}{{q  1}} = \left( {  11} \right) \times \frac{{{{\left( {  5} \right)}^8}  1}}{{\left( {  5  1} \right)}} = \left( {  11} \right) \times \frac{{390625  1}}{{\left( {  5  1} \right)}} = ...?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes its positive negative times negative

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks! Can you help me with my next question

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What is the 7th term of the geometric sequence where a1 = 1,024 and a4 = 16? 1 0.25 1 0.25

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1we have the subsequent formulas: \[\begin{gathered} {a_4} = {a_1}{q^3} \hfill \\ {a_7} = {a_1}{q^7} \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so we can rewrite the first formula as below: \[ \Large  16 = 1024 \times {q^3}\] please solve for q

anonymous
 one year ago
Best ResponseYou've already chosen the best response.016/1024 = 1024 x q^3/1024 .015625=q^3 (3)sqrt(.015625)=(3)sqrt(q^3) q=.53860

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the computation .015625=q^3 is right, so we have: \[\large q = \sqrt[3]{{  0.015625}} = ...?\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I got: q=1/4 am I right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh I got it now, I forgot to put the negative on the calculator

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1ok! Now we have: \[\Large {a_7} = {a_1}{q^7} = 1024 \times {\left( {  \frac{1}{4}} \right)^7} = ...?\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1sorry, I got another result

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1yes! \[\Large {a_7} =  0.0625 =  \frac{1}{{16}}\]
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