SOLUTION: 3;5;11;21 Determine the value of the 48th term

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Question 1107256: 3;5;11;21
Determine the value of the 48th term

Found 2 solutions by Boreal, math_helper:
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
differences between them are 2, 6, 10
differences between THOSE ARE 4 4
When two iterations are needed, this is n^2 and a QUADRATIC SEQUENCE
the coefficient of the square term is half of the difference or 2, so 2n^2
Now make a table

---n--n^2--2n^2 difference between original and 2n^2-----2n^2-4n+5
3--1 1 2 1 3
5--2 4 8 -3 5
11-3 9 18 - 7 11
21-4 16 32 -11 21
Those differences form an arithmetic series of -4n+5
The sequence is 2n^2-4n+5
the 48th term is 2(48)^2-48(4)+5=4421 ANSWER

Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website!

n diff diff(diff) 1 3 2 5 2 3 11 6 4 4 21 10 4

So if we assume
we can write
(1)
(2)
(3)
This system can be solved to get , , and
giving ; n = 1,2,3,�
and
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There is probably a method to solve this using z-transforms but I'm very rusty on them.