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Cambridge Further Maths: Sequences and Series.

A sawmill receives an order requesting many logs of various specific lengths that must come from the same particular tree. The log lengths must start at 5cm long and increase by 2 each time, up to a length of 53cm. The saw blade destroys 1cm (in length) of wood (turning it into sawdust) at every cut. What is the minimum height of the tree required to fulfill this order?
Please help.
Original post by Punextended
A sawmill receives an order requesting many logs of various specific lengths that must come from the same particular tree. The log lengths must start at 5cm long and increase by 2 each time, up to a length of 53cm. The saw blade destroys 1cm (in length) of wood (turning it into sawdust) at every cut. What is the minimum height of the tree required to fulfill this order?
Please help.

What have you done so far?
Original post by Plücker
What have you done so far?

I don't know how to express the series algebraically.
But it should be something like 5+1+7+1+9+...+1+53
Now the trouble for me in connecting all of this and putting it down on paper.
Original post by Punextended
I don't know how to express the series algebraically.
But it should be something like 5+1+7+1+9+...+1+53
Now the trouble for me in connecting all of this and putting it down on paper.


Well part of that is an AP, and part isn't, so why not separate the two out into two separate sequences?
Original post by ghostwalker
Well part of that is an AP, and part isn't, so why not separate the two out into two separate sequences?

Thank you! I finally got it.
Original post by Punextended
Thank you! I finally got it.


Cool.

Alternatively, you could have included the wasted material from the cut with the desired length, so you'd have 6+8+10+...+54, an AP. And subtract one at the end as the last cut would produce the final two pieces and you don't need a separate cut for the last piece - if the tree was a minimum length.
Reply 6
Avatar for realed
realed
9
i just added all the numbers from 6 to 54 and minused 1 but could you tell me if there's a quicker way of doing that
Original post by ghostwalker
Cool.

Alternatively, you could have included the wasted material from the cut with the desired length, so you'd have 6+8+10+...+54, an AP. And subtract one at the end as the last cut would produce the final two pieces and you don't need a separate cut for the last piece - if the tree was a minimum length.
Original post by realed
i just added all the numbers from 6 to 54 and minused 1 but could you tell me if there's a quicker way of doing that


If you just added them one at a time, then yes there's a quicker way. You have an arithmetic progression, so use the formulae.
Reply 8
Avatar for realed
realed
9
Original post by ghostwalker
If you just added them one at a time, then yes there's a quicker way. You have an arithmetic progression, so use the formulae.


what formulae
Original post by realed
what formulae


Have you not covered arithmetic progressions yet?

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