Please can you help me find the formula and the 9 th term for sequence's involving decimal's?
Please can you help me find the formula and the 9 th term for sequence's involving decimal's. Eg 2.75, 5.25, 7.75, 10.25, 12.75, 15.25. Another example is 6.6, 11.6, 18.6, 27.6, 38.6, 51.6, 66.6. Can you show me some more example's and explanation's of how to work out the formula and 9 th term of sequence's involving decimal's.
Answers:
9th term is 22.75 your adding 2.5 to each number
(2.75+2.5 = 5.25)
9th term is 102.6 your going up using 5,7,9,11,13,15,17,19 etc
(6.6 + 5 = 11.6) (11.6+7=18.6)
the 9th term is the 9th set of numbers
No work it out 4 yourself
The first one is very easy. evary number is the previous one plus 2.5. to discover it you only have the check the difference between tow consecutive numbers. So it is 2.75, 5.25, 7.75, 10.25, 12.75, 15.25, 17.75, 20.25, 22.75.
The second one is almost as easy, int this case the diference between the number changes (5, 7, 9, 11, 13, 15) so it´s easy to suppose that the eight number is the seventh plus 17 (66.6 +17 = 83.6) and the ninth number is the eigth plus plus 19 (83.6 + 19 = 102.6).
Keep trying and you'll get the skill.
2.75, 5.25, 7.75, 10.25, 12.75, 15.25
Look at the increase from 2.75 to 5.25, it's 2.75 + 2.5
Look at the increase from 5.25 to 7.75, it's 5.25 + 2.5
Each term increases by 2.5, so that is your rule.
The next term after 15.25 would be 17.75, 20.25, 22.75, 25.25, etc
Make sense?
6.6, 11.6, 18.6, 27.6, 38.6, 51.6
Look at the increase from 6.6 to 11.6, it's 6.6 + 5
Look at the increase from 11.6 to 18.6, it's 11.6 + 7
Look at the increase from 18.6 to 27.6, it's 18.6 + 9
Look at the increase from 27.6 to 38.6, it's 27.6 + 11
Do you see a pattern emerging? Each time you add on two more than you added the previous time.
So the term after 66.6 would be 83.6, 102.6, 126.6, etc
Make sense?
If you're looking for FORMULAS--here they are!
The first is .25 + 2.50n..So, the 9th term is .25 + 2.50(9)=.25 + 22.50=22.75. Still working on the second. Since the amt. added each time changes, there is some catch to that formula.Ok.I got it...(2n + 3) + y.where n is the term and y is the value of that term!
There are no apostrophes required in plurals. Decimals, Sequences, Explanations.
The first one just adds 2.5 to the previouse term.
2.75+2.5=5.25
5.25+2.5=7.75
etc.
so the 9th term is 22.75
The second example is a little more tricky. The second term adds 5, the third adds 7, the fourth adds 9, etc.
To figure these problems out you have to look for some kind of pattern.
The easiest method I have come across is to write out the sequence and then work out the difference bettween each term in it, if this is the same each time then the formula for the n th term would be d*n+a where d is the difference and a is a constant equal to the first term minus the difference. so the n th term in your first example is 2.5*n+0.25
If the difference changes each time then you need to work out the differences between them, this then gives a more complex formula, the complexity of the formula relates to the level you have to go too to get a constant (or rotating) difference. In your second example the difference increases by 2 each time, this gives you a formula for the n th term of (n^2)+2*n+3.6 we know the n^2 is needed because the difference changes by a fixed amount, if it changed by an amount that varied we would need n^x where x is the number of levels of change, the 2*n is because the change also has a 2 in it, and then the 3.6 is your constant again
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Answers:
9th term is 22.75 your adding 2.5 to each number
(2.75+2.5 = 5.25)
9th term is 102.6 your going up using 5,7,9,11,13,15,17,19 etc
(6.6 + 5 = 11.6) (11.6+7=18.6)
the 9th term is the 9th set of numbers
No work it out 4 yourself
The first one is very easy. evary number is the previous one plus 2.5. to discover it you only have the check the difference between tow consecutive numbers. So it is 2.75, 5.25, 7.75, 10.25, 12.75, 15.25, 17.75, 20.25, 22.75.
The second one is almost as easy, int this case the diference between the number changes (5, 7, 9, 11, 13, 15) so it´s easy to suppose that the eight number is the seventh plus 17 (66.6 +17 = 83.6) and the ninth number is the eigth plus plus 19 (83.6 + 19 = 102.6).
Keep trying and you'll get the skill.
2.75, 5.25, 7.75, 10.25, 12.75, 15.25
Look at the increase from 2.75 to 5.25, it's 2.75 + 2.5
Look at the increase from 5.25 to 7.75, it's 5.25 + 2.5
Each term increases by 2.5, so that is your rule.
The next term after 15.25 would be 17.75, 20.25, 22.75, 25.25, etc
Make sense?
6.6, 11.6, 18.6, 27.6, 38.6, 51.6
Look at the increase from 6.6 to 11.6, it's 6.6 + 5
Look at the increase from 11.6 to 18.6, it's 11.6 + 7
Look at the increase from 18.6 to 27.6, it's 18.6 + 9
Look at the increase from 27.6 to 38.6, it's 27.6 + 11
Do you see a pattern emerging? Each time you add on two more than you added the previous time.
So the term after 66.6 would be 83.6, 102.6, 126.6, etc
Make sense?
If you're looking for FORMULAS--here they are!
The first is .25 + 2.50n..So, the 9th term is .25 + 2.50(9)=.25 + 22.50=22.75. Still working on the second. Since the amt. added each time changes, there is some catch to that formula.Ok.I got it...(2n + 3) + y.where n is the term and y is the value of that term!
There are no apostrophes required in plurals. Decimals, Sequences, Explanations.
The first one just adds 2.5 to the previouse term.
2.75+2.5=5.25
5.25+2.5=7.75
etc.
so the 9th term is 22.75
The second example is a little more tricky. The second term adds 5, the third adds 7, the fourth adds 9, etc.
To figure these problems out you have to look for some kind of pattern.
The easiest method I have come across is to write out the sequence and then work out the difference bettween each term in it, if this is the same each time then the formula for the n th term would be d*n+a where d is the difference and a is a constant equal to the first term minus the difference. so the n th term in your first example is 2.5*n+0.25
If the difference changes each time then you need to work out the differences between them, this then gives a more complex formula, the complexity of the formula relates to the level you have to go too to get a constant (or rotating) difference. In your second example the difference increases by 2 each time, this gives you a formula for the n th term of (n^2)+2*n+3.6 we know the n^2 is needed because the difference changes by a fixed amount, if it changed by an amount that varied we would need n^x where x is the number of levels of change, the 2*n is because the change also has a 2 in it, and then the 3.6 is your constant again
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