MEI AS Further Maths Help (Sequences and Series)

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Sid2001
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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?


So far, I have produced the following expression.
Image



I'm not sure how I would proceed. The answer at the back of the book is 749cm. I think the part I am stuck on is forming an expression for the second part of the problem, "The saw blade destroys 1cm (in length) of wood at every cut."

Any help would be appreciation, thank you!
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mqb2766
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(Original post by Sid2001)
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?


So far, I have produced the following expression.
Image



I'm not sure how I would proceed. The answer at the back of the book is 749cm. I think the part I am stuck on is forming an expression for the second part of the problem, "The saw blade destroys 1cm (in length) of wood at every cut."

Any help would be appreciation, thank you!
Don't think your first sum (on the left hand side) is right. It would go
7+8+9+10+ ... +55
rather than
5 + 1 + 7 + 1 + 9 + .... + 1 + 53
Work out many cuts are made (fence posts/panels), and put it into a sum and evalaute or use the idea of triangular numbers for evaluating the sum.
Last edited by mqb2766; 1 year ago
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