Find the first three terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.an = –n2 + 4n − 8

Question

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

$a_n = -n^2 + 4n - 8$

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Solution

Sure, let's find the first three terms of the sequence defined by the formula an = -n^2 + 4n - 8.

For n = 1, substitute n = 1 into the formula: a1 = -(1)^2 + 4*1 - 8 = -1 + 4 - 8 = -5
For n = 2, substitute n = 2 into the formula: a2 = -(2)^2 + 4*2 - 8 = -4 + 8 - 8 = -4
For n = 3, substitute n = 3 into the formula: a3 = -(3)^2 + 4*3 - 8 = -9 + 12 - 8 = -5

So, the first three terms of the sequence are -5, -4, -5.

This problem has been solved

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