SOLUTION: An arithmetic and geometric series both have the same first terms,a=9. The fifth term of the arithmetic series is equal to the second term of the geometric series minus 1. The sum
Algebra ->
Sequences-and-series
-> SOLUTION: An arithmetic and geometric series both have the same first terms,a=9. The fifth term of the arithmetic series is equal to the second term of the geometric series minus 1. The sum
Log On
Question 1070260: An arithmetic and geometric series both have the same first terms,a=9. The fifth term of the arithmetic series is equal to the second term of the geometric series minus 1. The sum of first three terms of the geometric series is equal to the twenty eighth term of the arithmetic series. Find the ratio and common difference for each of the series(if the common difference is a whole number) Answer by ikleyn(52787) (Show Source):
You can put this solution on YOUR website! .
An arithmetic and geometric series both have the same first terms,a=9. The fifth term of the arithmetic series is equal to
the second term of the geometric series minus 1. The sum of first three terms of the geometric series is equal to the twenty eighth term
of the arithmetic series. Find the ratio and common difference for each of the series(if the common difference is a whole number)
~~~~~~~~~~~~~~~~~~~~~
9 + 4d = 9r-1, (1) ("The fifth term of the arithmetic series is equal to the second term of the geometric series minus 1")
9*(1+r+r^2) = 9 + 27d. (2) ("The sum of first three terms of the geometric series is equal to the twenty eighth term
of the arithmetic series.")
---->
4d = 9r - 10 , (3)
r + r^2 = 3d. (4)
---->
12d = 27r - 30, (5)
4r + 4r^2 = 12d. (6)
---->
4r + 4r^2 = 27r - 30 ---> 4r^2 - 23r + 30 = 0 ---> = = .
The only INTEGER root is r = = = 2.
Then d = = = 2.
Answer. r = 2. d = 2.
