# Geometric and arithmetic progression

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Thread starter 6 years ago
#1
Find x and y given that x+3y, 4 and 2x+ 2y are consecutive terms of a geometric series

and x+4y, 4 and x-2y are consecutive terms of an arithemtic series

I'm not even sure how to start
0
6 years ago
#2
(Original post by bl64)
Find x and y given that x+3y, 4 and 2x+ 2y are consecutive terms of a geometric series

and x+4y, 4 and x-2y are consecutive terms of an arithemtic series

I'm not even sure how to start
For an arithmetic sequence the difference between any term and the previous term is a constant. Can you use that to write an equation?
0
6 years ago
#3
(Original post by bl64)
Find x and y given that x+3y, 4 and 2x+ 2y are consecutive terms of a geometric series

and x+4y, 4 and x-2y are consecutive terms of an arithemtic series

I'm not even sure how to start
For three consecutive terms in an arithmetic sequence the middle term is
arithmetic mean of the other two terms (the previous one and the following one)

For three consecutive terms in a geometric sequence the middle term is
geometric mean of the other two terms (the previous one and the following one)

arithmetic mean of A and B is:

geometric mean of A and B is:

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