Question

The table shows the change in position of an object after it was launched straight up into the air.

Time
in seconds Total Distance in
Meters,
1 5
2 20
3 45
4 80
5 125
3) Part 1: Show the work needed to prove whether the table is an arithmetic sequence. Show work for credit

Part 2: Is the relationship between time and distance an arithmetic sequence? Answer in a complete sentence

Answer 1

Part 1 — Work to test for an arithmetic sequence:

An arithmetic sequence has a constant difference between consecutive terms. The given distances (in meters) are:
a1 = 5, a2 = 20, a3 = 45, a4 = 80, a5 = 125.

Compute the consecutive differences:
a2 − a1 = 20 − 5 = 15
a3 − a2 = 45 − 20 = 25
a4 − a3 = 80 − 45 = 35
a5 − a4 = 125 − 80 = 45

The differences are 15, 25, 35, 45, which are not all equal. Therefore the sequence is not arithmetic.

(As an extra note: the second differences are 25−15 = 10, 35−25 = 10, 45−35 = 10, which are constant — this indicates a quadratic-type relationship, not an arithmetic one.)

Part 2 — Complete-sentence answer:

No, the relationship between time and distance is not an arithmetic sequence because the differences between consecutive distances (15, 25, 35, 45) are not constant.