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Quadratic Sequence Challenge

You can find the nth term by plugging a given number into each equation. Start with 0 and then 1, 2, 3….. A number sequence begins to emerge.

$3 n^{2} + 3 n = 1$

$4 n^{2} + 2 n + 1$

$5 n^{2} + 3 n + 1$

$4 n^{2} + 4 n + 1$

$2 n^{2} + 8 n + 1$

$n^{2} + 7 n + 3$

$3 n^{2} - 2 n + 2$

$4 n^{2} - 2 n + 2$

$6 n^{2} - 5 n - 1$

$6 n^{2} - 5 n + 1$

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