Question

4. A stone nudged off the Royal Gorge Bridge near Cañon City, Colorado, falls 1053 feet before hitting water. Because its speed increases as it falls, the distance ittravels each second increases. During the first second, it drops 16 feet. During the next second, it drops an additional 48 feet. During the third second, it drops another80 feet. The distances traveled each second form an arithmetic sequence:16, 48, 80,...Part 1: How far does the stone fall during the 5th second? Find and use the explicitformula.a. What is the first term of the sequence?b. What is d, the common difference?c. Write the explicit formula in function notation. Use f(n) = f(1) + (n - 1)d, wheref(1) represents the first term.d. Use the explicit formula to find the distance the stone travels in the 5th second.Part II: The table below shows the values in the sequence you already know. Use the explicit formula or the common difference to complete the table for the first 7 seconds. Time (s) 1 2 3 4 5 6 7 Distance (ft) 16 48 80 | | 144 | | | | Part ||| : Use the table from part 2 to answer the questions a. The values in the table form a(n)___ sequence and the term numbers are shownb. The term values are shown in the in the____row, and the term numbers are shown in the ___ row. c. This sequence is associated with a(n)___function d. The domain of the function is the set of time values:___

Answer 1

The formula for determining the nth term of an arithmetic sequence is expressed as

f(n) = f(1) + (n - 1)d

Where

f(1) represents the first term

d represents the common difference

n represents the number of terms

From the information given,

f(1) = 16

d = 48 - 16 = 80 - 48 = 32

a) The first term of the sequence is 16

b) the common difference is 32

c) The explicit is

f(n) = 16 + 32(n - 1)

d) To find the distance the stone travels in the 5th second, it means that n = 5

Thus

f(5) = 16 + 32(5 - 1)

f(5) = 16 + 32 * 4

f(5) = 144

the distance the stone travels in the 5th second is 144 feet