Answer:
Solution:
Using the Geometric Means Formula
[tex]a_{n} = a_{1}r^{n-1}[/tex]
Thus,
5, ___, ___, 566, looking for the 2nd term and the 3rd term. Now it becomes 4 terms.
Solve first the common ration using the formula above
[tex]a_{n} = a_{1}r^{n-1}[/tex]
566 = 5[tex]r^{3}[/tex]
566/5 = 5[tex]r^{3}[/tex]/5
113.2= [tex]r^{3}[/tex] or
[tex]r^{3}[/tex] =113.2
[tex]\sqrt[3]{r^{3} } = \sqrt[3]{113.2}[/tex]
r = [tex]\sqrt[3]{113.2}[/tex] , then
To obtain the 2nd term multiply the common ratio to the 1st term.
[tex]a_{2} =[/tex] 5([tex]\sqrt[3]{113.2}[/tex] ) = 5[tex]\sqrt[3]{113.2}[/tex]
To obtain the 3rd term multiply the 2nd term by the common ratio
[tex]a_{3}[/tex] = (5[tex]\sqrt[3]{113.2}[/tex] )([tex]\sqrt[3]{113.2}[/tex] )
= (5[tex]\sqrt[3]{(113.2){2} }[/tex] )
Thus,
5, 5[tex]\sqrt[3]{113.2}[/tex] , 5[tex]\sqrt[3]{(113.2)^{2} }[/tex] , 566
Thank you!
Step-by-step explanation:
