math
posted by Anonymous on .
help me with sequences problem.So if the sequence is 2,5,10,17,26
+3 +5 +7 +9 1st difference
+2 +2 +2 2nd difference
then the nth term can be worked out by writing out :
n 1 2 3 4
n squared 1 4 9 16
original sequence 2 5 10 17
nth term= n squared+1
but what about this question:
8, 10, 14, 20, 28
+2 +4 +6 +8
+2 +2 +2
n 1 2 3 4
n squared 1 4 9 16
original sequence 8 10 14 20 the number you have to add to n squared is different every time so does anybody know how too get the nth term for this sequence?

help me with sequences problem.So if the sequence is 2,5,10,17,26
+3 +5 +7 +9 1st difference
+2 +2 +2 2nd difference
then the nth term can be worked out by writing out :
n 1 2 3 4
n squared 1 4 9 16
original sequence 2 5 10 17
nth term= n squared+1
but what about this question:
8, 10, 14, 20, 28
+2 +4 +6 +8
+2 +2 +2
n 1 2 3 4
n squared 1 4 9 16
original sequence 8 10 14 20 the number you have to add to n squared is different every time so does anybody know how too get the nth term for this sequence?
With 2nd differences being equal, the general expression is of the form an^2 + bn + c
8, 10, 14, 20, 28
.+2. +4. +6. +8
...+2. +2. +2
a(1)^2 + b(1) + c = 8
a(2)^2 + b(2) + c = 10
a(3)^2 + b(3) + c = 14
a + b + c = 8
4a + 2b + c = 10
9a + 3b + c = 14
Solving, a = 1, b = 1 and c = 8.
Thus, the nth term derives from N = n^2  n + 8.