SOLUTION: If 5, x, y, z, 405 are the first term of a GP , find the value of x, y, z.

Algebra ->  Sequences-and-series -> SOLUTION: If 5, x, y, z, 405 are the first term of a GP , find the value of x, y, z.      Log On


   

Question 878901: If 5, x, y, z, 405 are the first term of a GP , find the value of x, y, z.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
In a GP (a geometric progression or geometric sequence) each term is equal to the previous multiplied times a constant often called the common factor and represented by r .

MENTAL MATH (not showing the works of your quick mind):
The GP started with 5, and after multiplying times r four times we get
5r%5E4=405=810%2F2=10%2A81%2F2%2A5=5%2A81=5%2A3%5E4 so r=3 ,
which makes
x=5%2A3=highlight%2815%29
x=15%2A3=highlight%2845%29
y=45%2A3=highlight%28135%29
z=135%2A3=highlight%28405%29

SHOW YOUR WORK:
Teachers like to see formulas, and formulas are an efficient way to describe ideas and concepts. What you can think through in 5 seconds can be written in formulas in 5 minutes, while it would take much longer to write an explanation of the calculations in paragraph form. However, using formulas to communicate requires sharing a common symbolic language, and we may be used to different languages.
b%5B1%5D= first term of the GP.
r= common ratio of the GP.
b%5Bn%5D=b%5B1%5Dr%5E%28n-1%29=n%5Eth term of the GP.

b%5B1%5D=5
b%5B5%5D=405
5r%5E%285-1%29=405
5r%5E4=405
r%5E4=405%2F5
r%5E4=81
r=root%284%2C81%29
r=3
x=b%5B2%5D=5%2A3%5E%282-1%29=5%2A3%5E1=5%2A3=highlight%2815%29
y=b%5B3%5D=5%2A3%5E%283-1%29=5%2A3%5E2=5%2A9=highlight%2845%29
z=b%5B4%5D=5%2A3%5E%284-1%29=5%2A3%5E3=5%2A27=highlight%28135%29