SOLUTION: answer for what is the sixteen term in the following sequence? 1,2,4,7,11,16,22 t1=1, t2=2 Difference between the two sequence is greater than one from the differnce between t

Put them in a column.  Out beside each number write what
you get whe you subtract each number from the one just below it.
Then make a third column doing that with the second column

 1   1   1 
 2   2   1
 4   3   1
 7   4   1
11   5   1
16   5
22

Those columns are called the first and second differences.

Since it takes 2 columns of differences to get a column that has 
all the same number, we assume a polynomial of degree 2 for the 
nth term .



Substitute n=1



and since the first term is 1, we can write

 or



Substitute n=2



and since the second term is 2, we can write

 or



Substitute n=3



and since the third term is 4, we can write

 or



Now we have a system of equations



Solve that system and get ,,

So the nth term,

  

becomes



or if you prefer you can get an LCD



Then for the 16th term, we substitute n=16

 =  = 

Checking:

1,2,4,7,11,16,22,29,37,46,56,67,79,92,106,121

Edwin