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 Post subject: 100th term?Posted: Mon Jun 23, 2008 4:37 pm

Joined: Mon Feb 20, 2006 1:29 pm
Posts: 1805
Location: Berkshire
In this sequence what would be the 100th term?

2,9,16,23.....?

any ideas on working this one out, much appreciated

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 Post subject: Posted: Mon Jun 23, 2008 4:49 pm
I think it's 7n-5, so the answer would be 695 - I hope that's right!

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 Post subject: Posted: Mon Jun 23, 2008 4:50 pm

Joined: Tue Dec 13, 2005 12:49 pm
Posts: 1647
Location: berkshire
possibly....

I think .... as the difference between the number is 7 then the equation for the sequence will be 7n-5 (where n = the term)

therefore
1st tern 7x 1 -5 = 2
2nd term 7x 2 -5 = 9
3rd term 7 x 3 - 5 = 16.... and so on

meaning the 100th term

7 x 100 - 5 = 695

maybe

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 Post subject: Posted: Mon Jun 23, 2008 4:51 pm

Joined: Tue Dec 13, 2005 12:49 pm
Posts: 1647
Location: berkshire
Tipsy.... snap

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 Post subject: Posted: Mon Jun 23, 2008 5:12 pm

Joined: Mon Feb 20, 2006 1:29 pm
Posts: 1805
Location: Berkshire
cheers folks

but......where did you get the initial equation 7n-5?

i.e. if I came across a similar question, what is the best way to find the equation?

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 Post subject: Posted: Mon Jun 23, 2008 5:19 pm
I just worked it out by messing about with the numbers. I don't know if there is a sequence calculator online - how fabulous would that be!

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 Post subject: Posted: Mon Jun 23, 2008 5:44 pm

Joined: Tue Dec 13, 2005 12:49 pm
Posts: 1647
Location: berkshire
it is a linear sequence.... a sequence that increases or decreases by a constant.... the difference between the numbers is the first part of the equation.
If there was '2' between the numbers ie. 1,3,5,7,9 then the equation would start 2n.... then if you look at the sequence and apply the first term then 2 x 1 = 2 therefore the equation must be 2n - 1 to give you the first number in the sequence. check with the second term... 2 x 2 -1 = 3..... and so on.

You can also get a quadratic sequence i.e. 2 5 10 17 26... the sequence doesn't go up by a constant number... the equation for this one would be n squared + 1.....so the Usborne illustrated dictionary of Maths says (pg10)

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 Post subject: Posted: Mon Jun 23, 2008 5:56 pm
Chad - you are my hero! Why the **** was I never taught that! I just had to spend too many hours playing about with the numbers until I got it - grrrrrrr.

So give me an example if the term is cubed or squared, what would a sequence look like. So in 1,4,9,16 the gap is always 2 more - is that a clue?

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 Post subject: Posted: Mon Jun 23, 2008 6:10 pm

Joined: Mon Feb 20, 2006 1:29 pm
Posts: 1805
Location: Berkshire
Thankyou

Will check pg10 Chad. Had a quick look, earlier, but nothing leapt out.

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 Post subject: Posted: Mon Jun 23, 2008 7:23 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 13029
If it is a sequence based on n squared the second difference will be constant.

i.e. 2 5 10 17 26

if we look at the 'gaps' they are

3 5 7 9

and the gaps between them are always 2 so the rule starts 'n squared'' (you always have this gap to find how many n squared)

I'll try to find a good link to explain the rest!

http://www.bbc.co.uk/schools/gcsebitesi ... rev2.shtml

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