Sequences and Series Question?

[wildareal]

The side lengths of a right-angled triangle form the successive terms of an arithmetic sequence. The perimeter of the triangle is 72m. What are the side length of the triangle?

[cltf]

OK lets the sequence be: x, x+y, x+2y
therefore: s3 = 72
therefore: 72=3/2(2x+(3-1)y)
144=6x+6y
24=x+y
therefore your middle number is 24.
hence: 24-y,24,24+y
and well the next part was really guess and check for me. I can't remember the formula.

[luken93]

ha just guessed 23.24.25 haha

[physics]

that was a uni maths question on our SAC i think... but i have no idea how it is related to sequecnes and series though XD

[luken93]

that was a uni maths question on our SAC i think... but i have no idea how it is related to sequecnes and series though XD

you've gotta be joking thats a uni maths question, they were the first numbers that came to mind, because i knew it had to be odd even odd and divided by 3 = 72 so i guessed those three?

surely it isn't that hard?

dont mark my words but isnt it just:










consecutive numbers

[luken93]

The side lengths of a right-angled triangle form the successive terms of an arithmetic sequence. The perimeter of the triangle is 72m. What are the side length of the triangle?

when its successive terms doesnt that mean +1? and arithmetic sequence means it is limited to + or -?

doing this chap next term, this was just my memory of year 10 further unit 2

[m@tty]

No successive terms means they follow in the series.

Eg. 1, 4, 6, 8, 14, 20, 234709123864716239764023875

14, 20 and 234709123864716239764023875 are consecutive terms in the sequence.

Arithmetic sequence means where d is any constant.

EDIT:
So this problem is:







So this is the middle term, sub this into the original equation.

And now I get to the same part as the other guy....

[luken93]

No successive terms means they follow in the series.

Eg. 1, 4, 6, 8, 14, 20, 234709123864716239764023875

14, 20 and 234709123864716239764023875 are consecutive terms in the sequence.

Arithmetic sequence means where d is any constant.

woops haha, oh well i'll discover that next term/these holidays if i can be bothered.
have a lot of "if i can be bothered" tasks for the holidays haha

[luken93]

so in other words the middle term is 24 and the other two can be any equal value of y if it were

so it could be like 22/24/26 or 21/24/27 etc etc.
is there any real answer?

[m@tty]

But the triangle is right angled.

Therefore, the numbers must form a Pythagorean triplet.

[cltf]

that was a uni maths question on our SAC i think... but i have no idea how it is related to sequecnes and series though XD

you've gotta be joking thats a uni maths question, they were the first numbers that came to mind, because i knew it had to be odd even odd and divided by 3 = 72 so i guessed those three?

surely it isn't that hard?

dont mark my words but isnt it just:










consecutive numbers

It has to be a right angled triangle.
23,24,25 isn't a Pythagorean triad
21,24,27 isn't
22,24,26 isn't

18,24,30 is thought. - it was guess and check.

[the.watchman]

Yeah, it must be right angled and the side lengths are not necessarily one apart

Here's my solution from the spesh board:

AND ,    ,   

So

,   

SO the lengths are 18m, 24m and 30m

OR to replace step 2:

AND



,   

[cltf]

I feel like such an idiot, for not figuring out that step....