What is the next term in the sequence below?
2 answers:
Answer: Option a.
Step-by-step explanation:
1. The sequence shown in the problem is a Geometric sequence, because it has a common ratio. This means that when you multiply one of those numbers by the common ratio, you obtain the next number.
2. Then, you can calculate the common ratio as following:
3. Therefor, the next term is:
You might be interested in
You know 1 is not a root because the sum of the coeffcients of the equation is 14, not zero.
It is fairly easy to try 3 by synthetic division (see attachment), which tells you that 3 is a root and the remaining quadratic factor is x²-3x-5. The quadratic formula tells you the roots of that factor are
... x = (-b±√(b²-4ac))/(2a) = (3±√29)/2
The appropriate choices are
... C. (3-√29)/2
... D. (3+√29)/2
... F. 3
_____
The quadratic formula tells you the solution to
... ax²+bx+c=0
is x = (-b±√(b²-4ac))/(2a)
We have a=1, b=-3, c=-5.
