+0

# Geometric series

0
91
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

Guest Aug 23, 2017

#1
+18715
+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
Sort:

#1
+18715
+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

### 14 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details