The Student Room Group

Arithmetic sequences

Howdy,
Is the below rule true?


For
ax + by = c
dx + fy = g,


if a, b, c, d, f, g form an arithmetic sequence, then (x, y) = (-1, 2)


I just can't find anything on the web for it
:colondollar:
Original post by makin
Howdy,
Is the below rule true?


For
ax + by = c
dx + fy = g,


if a, b, c, d, f, g form an arithmetic sequence, then (x, y) = (-1, 2)


I just can't find anything on the web for it
:colondollar:


If they do then

ax + (a+p)y = a+2p
(a+3p)x + (a+4p)y = a+5p

Can you go from there?
Reply 2
Original post by makin
Howdy,
Is the below rule true?


For
ax + by = c
dx + fy = g,


if a, b, c, d, f, g form an arithmetic sequence, then (x, y) = (-1, 2)


I just can't find anything on the web for it
:colondollar:

That's true assuming the common difference is not 0. If it's 0 then something else is true which I'll let you work out.

Do you need help with the proof?

EDIT: Tenofthem has shown you how to start off.
Reply 3
Original post by TenOfThem
If they do then

ax + (a+p)y = a+2p
(a+3p)x + (a+4p)y = a+5p

Can you go from there?


Original post by notnek
That's true assuming the common difference is not 0. If it's 0 then something else is true which I'll let you work out.

Do you need help with the proof?

EDIT: Tenofthem has shown you how to start off.



Thanks for the help :smile:.

I should be okay, with what you have both given me.

Have a nice weekend
Reply 4
lol this is exactly my homework. I had four to choose from and I picked this one because the proof was easy XD

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