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Hi, I start doing the task, but then I dont know what to do next. Here is:

 

1a+a2+a3=62

a1*a2*a3=1000

 

a1+a1*q+a1*q^2=62

a1*a1*q*a1*q^2=1000

 

a1+a1*q+a1*q^2=62

a1^3 * q^3=1000

 Aug 23, 2017

Best Answer 

 #1
avatar+22172 
+2

Geometric series

Hi, I start doing the task, but then I dont know what to do next. Here is:

a1+a2+a3=62

a1*a2*a3=1000

 

\(\begin{array}{|rcll|} \hline a_1*a_2*a_3 &=& 1000 & | \quad a_1 = a \qquad a_2 = a*q \qquad a_3 = a*q^2 \\ a*(a*q)*(a*q^2) &=& 1000 \\ a^3*q^3 &=& 1000 \\ a^3*q^3 &=& 10^3 & | \quad \sqrt[3]{} \\ a*q &=& 10 \\ \mathbf{ a} &\mathbf{ =}&\mathbf{ \frac{10}{q} }\\\\ a_1+a_2+a_3 &=& 62 & | \quad a_1 = a \qquad a_2 = a*q \qquad a_3 = a*q^2 \\ a +a*q + a*q^2 &=& 62 \\ a *(1 + q + q^2) &=& 62 & | \quad \mathbf{a= \frac{10}{q}} \\ \frac{10}{q} *(1 + q + q^2) &=& 62 \\ \frac{1}{q} *(1 + q + q^2) &=& 6.2 \\ \frac{1}{q} +1+q &=& 6.2 \\ \frac{1+q^2}{q} &=& 5.2 \\ 1+q^2 &=& 5.2*q \\ q^2-5.2*q +1 &=& 0 \\ (q-5)*(q-0.2) &=& 0 \\\\ \mathbf{q = 5} &\mathbf{ \text{ or } }& \mathbf{q = 0.2 }\\\\ a =\frac{10}{5} && a =\frac{10}{0.2} \\ \mathbf{a = 2} &\mathbf{ \text{ or } }& \mathbf{a = 50} \\ \hline \end{array} \)

 

Geometric series:

 

1.

\(a=2 \quad q = 5 : \\ 2+2*5+2*5^2 = 62\ \checkmark \\ 2*(2*5)*(2*5^2) = 1000\ \checkmark \)

 

2

.\(a=50 \quad q = 0.2 : \\ 50 + 50*0.2 + 50*0.2^2 = 62 \ \checkmark \\ 50*(50*0.2)*(50*0.2^2) = 1000\ \checkmark \)

 

 

laugh

 Aug 23, 2017
 #1
avatar+22172 
+2
Best Answer

Geometric series

Hi, I start doing the task, but then I dont know what to do next. Here is:

a1+a2+a3=62

a1*a2*a3=1000

 

\(\begin{array}{|rcll|} \hline a_1*a_2*a_3 &=& 1000 & | \quad a_1 = a \qquad a_2 = a*q \qquad a_3 = a*q^2 \\ a*(a*q)*(a*q^2) &=& 1000 \\ a^3*q^3 &=& 1000 \\ a^3*q^3 &=& 10^3 & | \quad \sqrt[3]{} \\ a*q &=& 10 \\ \mathbf{ a} &\mathbf{ =}&\mathbf{ \frac{10}{q} }\\\\ a_1+a_2+a_3 &=& 62 & | \quad a_1 = a \qquad a_2 = a*q \qquad a_3 = a*q^2 \\ a +a*q + a*q^2 &=& 62 \\ a *(1 + q + q^2) &=& 62 & | \quad \mathbf{a= \frac{10}{q}} \\ \frac{10}{q} *(1 + q + q^2) &=& 62 \\ \frac{1}{q} *(1 + q + q^2) &=& 6.2 \\ \frac{1}{q} +1+q &=& 6.2 \\ \frac{1+q^2}{q} &=& 5.2 \\ 1+q^2 &=& 5.2*q \\ q^2-5.2*q +1 &=& 0 \\ (q-5)*(q-0.2) &=& 0 \\\\ \mathbf{q = 5} &\mathbf{ \text{ or } }& \mathbf{q = 0.2 }\\\\ a =\frac{10}{5} && a =\frac{10}{0.2} \\ \mathbf{a = 2} &\mathbf{ \text{ or } }& \mathbf{a = 50} \\ \hline \end{array} \)

 

Geometric series:

 

1.

\(a=2 \quad q = 5 : \\ 2+2*5+2*5^2 = 62\ \checkmark \\ 2*(2*5)*(2*5^2) = 1000\ \checkmark \)

 

2

.\(a=50 \quad q = 0.2 : \\ 50 + 50*0.2 + 50*0.2^2 = 62 \ \checkmark \\ 50*(50*0.2)*(50*0.2^2) = 1000\ \checkmark \)

 

 

laugh

heureka Aug 23, 2017

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