Each term is increased by adding five times three to an increasing exponent.
2 + 5 x 3 to the zero = 7 + 5 x 3 to the first = 22 + 5 x 3 squared = 67
The next term would be 202 which makes the rule something like
n = n + 5 x 3 to the x+1, but please double-check that.
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Each term is 6 more than the last term; ie add 6 to the current term to get the next term. U{n} = 6n + 4 for n = 1, 2, 3, 4
22/33 = 2/3
To find the nth term of a sequence, we first need to identify the pattern or rule governing the sequence. In this case, the sequence appears to be increasing by 9, then 13, then 17, and so on. This pattern indicates that the nth term is given by the formula n^2 + n - 1. So, the nth term of the sequence 0, 9, 22, 39, 60 is n^2 + n - 1.
As can be seen, each succesive term is 2 greater than the last. We can write a rule to calculate the nth term. Here the rule equals 2n - 8. So the 20th term = (2 * 20) - 8 = 32.
There are infinitely many possible answers. The only solution in the form a cubic polynomial is Un = (25n3 - 147n2 + 236n - 120)/12 for n = 1, 2, 3, 4