Determine the explicit form of the function that describes the sequence below. 16, 24, 36, 54, ...

A. f(n) = 8n + 8
B. f(n) = 16(3/2)^(n - 1)
C. f(n) = 3/2(n - 1) + 16
D. f(n) = 3/2(16)^(n - 1)

B. f(n) = 16(3/2)^(n - 1).

Step-by-step explanation:

You can just substitute values. For questions like these, I usually use the second or third value to try the equations, because most of the time, the people who made these problems would make them all work for the first or last values.

A: 8n + 8 = 8 * 3 + 8 = 24 + 8 = 32. 32 is not equal to 36, so you can eliminate A.

B: 16 (3/2)^ (n - 1) = 16 * (1.5)^ (3 - 1) = 16 * (1.5)^ 2 = 16 * 2.25 = 36. 36 = 36, so you can keep this choice... for now.

C: 3/2 (n - 1) + 16 = 1.5 * (3 - 1) + 16 = 1.5 * 2 + 16 = 3 + 16 = 19. 19 does not equal 36, so you can eliminate C.

D: 3/2 (16)^ (n - 1) = 1.5 * (16)^ (3 - 1) = 1.5 * 16^2 = 1.5 * 256 = 384. 384 does not equal 36, so you can eliminate D as well.

Since A, C, and D do not work, you can say that the explicit form of the function would be Choice B.

Just to be sure, you can check using all four values...

f(1) = 16 * (1.5)^0 = 16 * 1 = 16   TRUE

f(2) = 16 * (1.5)^1 = 16 * 1.5 = 24   TRUE

f(3) = 16 * (1.5)^2 = 16 * 2.25 = 36   TRUE

f(4) = 16 * (1.5)^3 = 16 * 3.375 = 54   TRUE

Since all of the values match up, you can be sure that Choice B is the right answer.

Hope this helps! :)

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step-by-step explanation:

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