Question

The table shows the balance in Jacqueline’s investment account each year for five years.

Year Investment
1 $20,000
2 $21,750
3 $23,500
4 $25,250
5 $27,000

2A) Part 1: Show the work needed to prove whether the table is an arithmetic sequence. Show work for credit.

Part 2: Does the table represent an arithmetic sequence?

Answer 1

Part 1 — Show work:
Compute the differences between consecutive terms.
- 21,750 − 20,000 = 1,750
- 23,500 − 21,750 = 1,750
- 25,250 − 23,500 = 1,750
- 27,000 − 25,250 = 1,750

Because each consecutive difference is the same (1,750), the sequence has a constant common difference.

Part 2 — Conclusion:
Yes. The table represents an arithmetic sequence with common difference d = 1,750.
The nth term is a_n = 20,000 + (n − 1)(1,750).