sequence
- Thread starter xc630
- Start date
Hello I would like some help with this following sequence. I need to find a recursive definition for it.
1,3,7,13,21,31,...
All I noticed is that for the 1st two terms it was 2(tn-1) +1 but after that it didn't work.
Any
n.....1.....2.....3.....4.....5.....6
N.....1.....3....7.....13...21...31
Duff.....2....4.....6.....8.....10
Diff........2......2.....2.....2
SInce the second differences are constant, you have a finite difference sequence of the second order the nth term of which is of the form an^2 + bn + c = 0
Using the data given:
a(1^2) + b(1) + c = 1 or a + b + c = 1
a(2&2) + b(2) + c = 3or 4a + 2b + c = 3
a(3^2) + b(3) + c = 7 or 9a + 3b + c = 7
Solving, a = 1, b = -1 and c = 1 giving the expression for the nth term of
N = n^2 - n + 1
1,3,7,13,21,31,...
All I noticed is that for the 1st two terms it was 2(tn-1) +1 but after that it didn't work.
Any
n.....1.....2.....3.....4.....5.....6
N.....1.....3....7.....13...21...31
Duff.....2....4.....6.....8.....10
Diff........2......2.....2.....2
SInce the second differences are constant, you have a finite difference sequence of the second order the nth term of which is of the form an^2 + bn + c = 0
Using the data given:
a(1^2) + b(1) + c = 1 or a + b + c = 1
a(2&2) + b(2) + c = 3or 4a + 2b + c = 3
a(3^2) + b(3) + c = 7 or 9a + 3b + c = 7
Solving, a = 1, b = -1 and c = 1 giving the expression for the nth term of
N = n^2 - n + 1