+0

# Geometric series

0
385
1

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

#1
+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

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

Aug 23, 2017

#1
+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

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

heureka Aug 23, 2017