100th term?
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100th term?
In this sequence what would be the 100th term?
2,9,16,23.....?
any ideas on working this one out, much appreciated
2,9,16,23.....?
any ideas on working this one out, much appreciated
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- Posts: 1806
- Joined: Mon Feb 20, 2006 2:29 pm
- 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)
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)
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?
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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- Posts: 1806
- Joined: Mon Feb 20, 2006 2:29 pm
- Location: Berkshire
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
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