Oh, what a lovely sequence you have there! To find the pattern, let's look at the differences between the numbers: 9, 13, 17, 21. Do you see how the differences are increasing by 4 each time? That means the nth term is found by adding the square of n to the previous term. Happy math-ing, my friend!
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To find the nth term of a sequence, we first need to identify the pattern. In this case, the differences between consecutive terms are 9, 13, 17, and 21. These differences do not form a simple arithmetic progression, so the sequence likely involves a quadratic equation. By analyzing the pattern further, we can determine the general formula for the nth term.
6 = 2 * 3
15 = 3 * 5
28 = 4 * 7
45 = 5 * 9
66 = 6 * 11
Assuming the pattern continues, the nth term is (n + 1) * (2n +1) = 2n^2 + 3n + 1.
nth term = 5 +8n
15(1)
Divide the sequence by 5 and the answer becomes very obvious: 1, 4, 9, 16,...N2 So, 5, 20, 45, 80,...5N2
5n+1
t(n) = 28-3n where n = 1,2,3,...