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###### Cambridge Further Maths: Sequences and Series.

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3 years ago

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.

Please help.

Reply 1

3 years ago

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.

Please help.

What have you done so far?

Reply 2

3 years ago

Original post by PlĆ¼cker

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.

Reply 3

3 years ago

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.

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?

Reply 4

3 years ago

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.

Reply 5

3 years ago

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.

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.

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 7

1 year ago

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.

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

Reply 9

1 year ago

Original post by realed

what formulae

Have you not covered arithmetic progressions yet?

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