Question

The table displays the speed of a car s, in feet per second, t seconds after it starts coasting.

Time, t (in seconds) Speed, s (ft/sec)
1 57
2 54.15
3 51.44
4 48.87
a) Explain why this sequence is geometric.

Answer 1

The student's question pertains to identifying a sequence as geometric by verifying if the ratio of consecutive terms is constant. The car's speeds form a geometric sequence because each term is obtained by multiplying the previous term by a common ratio, which in this case is approximately 0.95.

Step-by-step explanation:

The student's question about the speed of a car in feet per second at various seconds after it starts coasting seems to be asking why the given sequence is geometric. A geometric sequence is one where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. To prove if the given speeds represent a geometric sequence, we need to divide each term by the previous term to see if the ratio is constant.

For the given speed values:

• s(2)/s(1) = 54.15 / 57
• s(3)/s(2) = 51.44 / 54.15
• s(4)/s(3) = 48.87 / 51.44

By calculating, you would find that the ratio (rounding to two decimal places) remains the same at approximately 0.95 for each pair of consecutive terms, which confirms that the sequence of speeds is indeed geometric.