Find the geometric means in the following sequence.47,?,?,?,?, - 789, 929RSelect one:a. -6,580, -9,870, -13,160, -16,450b. 329, 2,303, 16,121, 112,847C. 2,303, -16,121, 112,847, -789,944d. -329, 2,303, -16,121, 112,847

Accepted Solution

Answer:d (last choice)Step-by-step explanation:The explicit form of a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1}[/tex] where [tex]a_1[/tex] is the first term while [tex]r[/tex] is the common ratio.We are given the first term [tex]a_1=47[/tex].We are given the sixth term [tex]a_6=-789929[/tex].If we divide 6th term by 1st term this is the result:[tex]\frac{a_1 \cdot r^5}{a_1 }=\frac{-789929}{47}[/tex]Simplify both sides:[tex]r^5=-16807[/tex]Take the fifth root of both sides:[tex]r=-7[/tex]The common ratio is -7.So all we have to do is start with the first term and keep multiplying by -7 to get the other terms.[tex]a_1=47[/tex][tex]a_2=47(-7)=-329[/tex][tex]a_3=47(-7)^2=2303[/tex][tex]a_4=47(-7)^3=-16121[/tex][tex]a_5=47(-7)^4=112847[/tex][tex]a_6=47(-7)^5=-789929[/tex]The terms -329,2303,-16121,112847 are what we are looking for in our choices.That's the last choice.