SOLUTION: hi, i need to know the between number 6, 13, ?, 33.And also for another one.The questions are, __?___,7, 26, 63. please reveal me as soon as possible

Algebra ->  Sequences-and-series -> SOLUTION: hi, i need to know the between number 6, 13, ?, 33.And also for another one.The questions are, __?___,7, 26, 63. please reveal me as soon as possible       Log On


   

Question 1055907: hi,
i need to know the between number
6, 13, ?, 33.And also for another one.The questions are,

__?___,7, 26, 63.
please reveal me as soon as possible

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
     
6, 13, ?, 33

An%5E2%2BBn%2BC=a%5Bn%5D

Substitute n=1, a1 = 6

A%281%29%5E2%2BB%281%29%2BC=a%5B1%5D=6
 
A%281%29%2BB%2BC=6

A%2BB%2BC=6

Substitute n=2, a2 = 13

A%282%29%5E2%2BB%282%29%2BC=a%5B2%5D=13
 
A%284%29%2B2B%2BC=13

4A%2B2B%2BC=13

Substitute n=4, a4 = 33

A%284%29%5E2%2BB%284%29%2BC=a%5B4%5D=33
 
A%2816%29%2B4B%2BC=33

16A%2B4B%2BC=33

Solve the system:

system%28A%2BB%2BC=6%2C4A%2B2B%2BC=13%2C16A%2B4B%2BC=33%29

and get A=1, B=4, C=1

So the formula is

n%5E2%2B4n%2B1=a%5Bn%5D  

Substitute n=3

%283%29%5E2%2B4%283%29%2B1=a%5B3%5D

9%2B12%2B1=a%5B3%5D

22=a%5B3%5D

6, 13, 22, 33 

-------------------------

__, __, 7, 26, 63.

An%5E2%2BBn%2BC=a%5Bn%5D

Substitute n=3, a3 = 7

A%283%29%5E2%2BB%283%29%2BC=a%5B3%5D=7
 
A%289%29%2B3B%2BC=7

9A%2B3B%2BC=7

Substitute n=4, a4 = 26

A%284%29%5E2%2BB%284%29%2BC=a%5B4%5D=26
 
A%2816%29%2B4B%2BC=26

16A%2B4B%2BC=26

Substitute n=5, a5 = 63

A%285%29%5E2%2BB%285%29%2BC=a%5B5%5D=63
 
A%2825%29%2B5B%2BC=63

25A%2B5B%2BC=63

Solve the system:

system%289A%2B3B%2BC=7%2C16A%2B4B%2BC=26%2C25A%2B5B%2BC=63%29

and get A=9, B=-44, C=58

So the formula is

9n%5E2-44n%2B58=a%5Bn%5D  

Substitute n=1

9%281%29%5E2-44%281%29%2B58=a%5B1%5D

9-44%2B58=a%5B1%5D

23=a%5B1%5D

Substitute n=2

9%282%29%5E2-44%282%29%2B58=a%5B2%5D

9%284%29-88%2B58=a%5B2%5D

36-88%2B58=a%5B1%5D

6=a%5B1%5D

23, 6, 7, 26, 63

Edwin