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Explicit formula?
Using iteration find the explicit formula for
t(sub k) = t(sub k-1) + 3k + 1, for all integers k >= 1
t(sub 0) = 0
Thanks for any help :)
1 Answer
- Anonymous1 decade agoFavourite answer
Use the recurrence relation to evaluate the first few terms of the sequence. Then use the method of differences and you will find that the second differences are constant. This tells you that the explicit formula for t is a quadratic function of k.
This means that you can use the first three terms and
k = 0, 1, 2 in the proposed formula ak^2 + bk + c to find the values of a, b, c. Of course k = 0 gives you c = 0 immediately so finding a and b is even easier. You will find that each is an integer + 1/2.