Aritmetic Sequence with variables

[peep1963]

Hi,
I can't figure this out I know the answe because it's an easy problem but I couldn't sole it if you asked me another one of these. Please if you know how to do this, I guess algebraically, show me.


Find x and y if the sequence y, 2x+y, 7y, 20, ...... is arithmetic.

I know that

y=2
2x+y=8
7y=14

so that y=2 and x=3 but how could I figure that out without just guessing?


Thanks!

 

[royhaas]

Any two consecutive terms of an arithmetic sequence have the same (constant) difference. Use that to generate two linear equations in two unknowns.

 

[royhaas]

Any two consecutive terms of an arithmetic sequence have the same (constant) difference. Use that to generate two linear equations in two unknowns.

 

[pav]

substitute

y=2 into

2x+y=8

then 2x+2=8

for the first each term respectivley

a,a+d,a+2d so notice the number of d is always one less the variable so we have

a+d(n-1)