maths gah, +REP

[Mitch4?]

okay, so far this year maths hasnt really been a problem, nearly finished c2 now and started to revise over everything i done, and i am looking at this question and just mega failing it, and cba to work it out cause ive tried lots of things.
anyone got any suggestions to what i should do?


"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 arithmetic series"

all help will be appreciated

[Soka]

is this for C2?

i'm assuming you use

Un = a + (n -1)d for arithmetic
Un = ar^(n-1) for geometric

firstly you need to work out ratio.. then use simultaneous equations. I'll do it now if you want. Can i check im reading question right:

Arithmetic = x + 4y, 4, x - 2y
Geometric = x + 3y, 4, 2x + 2y.

are they the sequences from the beginning with x + 4y, x + 3y as first terms or what?

[Soka]

OK.. i've had a crack at it and i've assumed that the sequences you've given are from first term So if it isn't this is wrong!

x + 3y, 4, 2x + 2y = geometric.. thus ratio = any term divided by previous term so (2x + 2y)/4 = 1/2x + 1/2y = ratio.

x + 4y, 4, x - 2y = arithmetic... thus common difference = any term minus previous term so (x - 2y) - 4 = x - 2y - 4 = common difference.

We know that

U2 = ar^(2-1) = ar.. so U2 = (x + 3y)(1/2x + 1/2y)
hence (x + 3y)(1/2x + 1/2y) = 4.

Also;

U2 = a + (n-1)d = a + d so U2 = (x + 4y) + (x - 2y - 4)
hence (2x + 2y - 4) = 4
rearranging gives..
2x + 2y = 8
2y = 8 - 2x
y = 4 - x

now subbing this into:

(x + 3y)(1/2x + 1/2y) = 4
(x + 3(4-x))(1/2x + 1/2(4-x)) = 4
(x +12 - 3x)(1/2x + 2 - 1/2x) = 4
(12 - 2x)(2) = 4
24 - 4x = 4
4x = 20
x = 5.. and putting x into y = 4 - x = 4 - 5 = -1
thus..
x = 5
y = -1.

all of this will be wrong if i've read question wrong haha. and there is probably a quicker way than all the stuff i've done.. my C2's a bit rusty

[Mitch4?]

Okay i'm going to look through that now
cheers thanks alot really appreciate it!!
It is C2 yeah,

i got the common differences and then got really confused haha.