Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain.

1 answer:

7 0

Using the formula:
an = a1 +(n-1)d
a1 = 9 (first term of the sequence)
d= -6 (common difference)

Substituting into the formula:
an= a1 +(n-1)d
an = 9 + (n-1)(-6)
an = 9 - 6(n-1)

So the best answer is :D. a_n = 9 − 6(n − 1) where n ≥ 1

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If you use the ATAN2( ) function of a graphing calculator or spreadsheet, it will give you the angle in the proper quadrant. If you use the arctangent function (tan⁻¹) of a typical scientific calculator, it will give you a 4th-quadrant angle when the ratio is negative. You must recognize that the desired 2nd-quadrant angle is 180° more than that.

It may help you to consider looking at the "reference angle." In this geometry, it is the angle between the vector v and the -x axis. The coordinates tell you the lengths of the sides of the triangle vector v forms with the -x axis and a vertical line from that axis to the tip of the vector. Then the trig ratio you're interested in is ...

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