arithmetic progression

A teacher illustrates arithmetic series by cutting a length of string into pieces so that the length of the pieces form an arithmetic series and the entire length of string is used up exactly.

a) A 1 metre length is cut so the first piece measures 30cm and the 4th 15 cm . Find the number of pieces

I found the common difference which was 5 but not sure how to go on from there

b) A 2m length is cut so that the first piece measures 2 cm and there are 8 pieces find the length of the longest piece

I didn't have any idea where to start on this one

Reply 1

lerjj

13

Original post by bl64

A teacher illustrates arithmetic series by cutting a length of string into pieces so that the length of the pieces form an arithmetic series and the entire length of string is used up exactly.

a) A 1 metre length is cut so the first piece measures 30cm and the 4th 15 cm . Find the number of pieces

I found the common difference which was 5 but not sure how to go on from there

b) A 2m length is cut so that the first piece measures 2 cm and there are 8 pieces find the length of the longest piece

I didn't have any idea where to start on this one

For a) write two columns out: the series, and the running total

For b) you're looking to find 8 equally spaced numbers that add up to 200.

Reply 2

bl64

OP

8

Original post by lerjj

For a) write two columns out: the series, and the running total

For b) you're looking to find 8 equally spaced numbers that add up to 200.

is there a quick way of working that out in a formula?

Reply 3

lerjj

13

Original post by bl64

is there a quick way of working that out in a formula?

What level of maths are you at? There are formulae, but you wouldn't be expected to know them at GCSE or lower I think.

Spoiler

(edited 9 years ago)

Reply 4

ghostwalker

17

Original post by bl64

I found the common difference which was 5 but not sure how to go on from there

Common difference is -5, not 5.

For the first one you can use the formula

S_n=\frac{n}{2}(2a+(n-1)d)

and for the second

S_n=\frac{n}{2}(a+l)

I presume you've come across these before.

In each case you know all the information in the formula bar one item - the one you're trying to work out. So, plug in the numbers and solve.

Using the formula on the first one will give you two solutions - one of which isn't valid. Have a think as to why.

(edited 9 years ago)

Reply 5

TenOfThem

18

Original post by bl64

A teacher illustrates arithmetic series by cutting a length of string into pieces so that the length of the pieces form an arithmetic series and the entire length of string is used up exactly.

a) A 1 metre length is cut so the first piece measures 30cm and the 4th 15 cm . Find the number of pieces

I found the common difference which was 5 but not sure how to go on from there

S_n = \dfrac{n}{2}[2a+(n-1)d]

You know everything apart from n

Reply 6

Nels98

2

Use the formula
Sn=0.5n[2a+(n-1)xd]
use simple algebra to rearrange into a quadratic then solve using the quadratic formula if need be. only one of the answers will be correct. it should be obvious which one that is.

arithmetic progression

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