Question

What function represents this arithmetic sequence? 32, 41, 50, . . .

Answer 1

The correct answer is f(x) = 9x + 23.

In order to find the answer, first make two ordered pairs using x as what number it is in the sequence and y as the value. Therefore you have the following ordered pairs: (1, 32) and (2, 41). Given that, we can find the slope by using the slope formula below.

m (slope) = (y2 - y1)/(x2 - x1)

m = (41 - 32)/(2 - 1)

m = 9/1

m = 9

Now that we have a slope of 9, we can find the intercept using slope intercept form and a point. We'll use (1, 32) as the point.

y = mx + b

32 = 1(9) + b

32 = 9 + b

23 = b

Now that we have the slope and intercept, we can write the equation.

f(x) = 9x + 23