Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.an = 6n2 + 9n − 6

Question

Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.

$a_n = 6n^2 + 9n - 6$

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Solution

Sure, let's find the first four terms of the sequence defined by the formula an = 6n^2 + 9n - 6.

For n = 1, a1 = 6(1)^2 + 9(1) - 6 = 6 + 9 - 6 = 9
For n = 2, a2 = 6(2)^2 + 9(2) - 6 = 24 + 18 - 6 = 36
For n = 3, a3 = 6(3)^2 + 9(3) - 6 = 54 + 27 - 6 = 75
For n = 4, a4 = 6(4)^2 + 9(4) - 6 = 96 + 36 - 6 = 126

So, the first four terms of the sequence are 9, 36, 75, and 126.

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