Arithmetic Sequences

Hey, Tried to do these questions but not enough variable for me to work it out...can you help me?

Q:- A piece of string 10M long is to be cut into pieces, so that the lengths of the pieces form an aritmetic sequences.

i) The length of the longest and the shortest pieces are 1m and 25cm respectivly; how many pieces are there?
ii) If the same string has been cut into 20 pieces with lenghts that formed an arithmetic sequences, and if the length of the second longest piece had been 92.5 cm, how long would the shortest piece have been?

Thanks for your time!
David :smile:

Reply 1

apple tree

I think there's a formula involving the first and last term, it's something like sum of n terms = n([first term] + [last term])/2
Try finding it, it's a good exercise to show how to arrive at the equations (I'll have a go myself for fun)

Reply 2

davidcy123

OP

apple tree

I think there's a formula involving the first and last term, it's something like sum of n terms = n([first term] + [last term])/2
Try finding it, it's a good exercise to show how to arrive at the equations (I'll have a go myself for fun)

well when you get the answer, can you help me?

Reply 3

apple tree

It helps doesn't it? For the first part of the question.

Reply 4

davidcy123

OP

is that the correct equation you gave me?

Reply 5

apple tree

you tell me, I think you should believe in your own working :smile:

.
The proof is easily found in textbooks, have you come across it?

Reply 6

davidcy123

OP

yes it work for part i) but part ii) is slightly more tricky...any luck?

Reply 7

apple tree

boils down to solving simultaneous equations, do you know any equations or expressions for terms in arithmetic series?

Reply 8

nota bene

15

davidcy123

Hey, Tried to do these questions but not enough variable for me to work it out...can you help me?

Q:- A piece of string 10M long is to be cut into pieces, so that the lengths of the pieces form an aritmetic sequences.

i) The length of the longest and the shortest pieces are 1m and 25cm respectivly; how many pieces are there?
ii) If the same string has been cut into 20 pieces with lenghts that formed an arithmetic sequences, and if the length of the second longest piece had been 92.5 cm, how long would the shortest piece have been?

Thanks for your time!
David :smile:

i) Sn=(n/2)(U1+Un) where Sn is the sum of all terms, n is the number of terms, U1 is the first term and Un is the last term

hence 10=(n/2)(0.25+1)
solve and n=16

ii) use the formulae Un=U1+(n-1)d where d is the common difference and n is the nth term of the sequence and U1 is the first term...

and use the formula used in i) (though another version) Sn=(n/2)(2U1+(n-1)d)

Arithmetic Sequences

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