Question

Select ALL of the following that are examples of an arithmetic sequence.
A. 1, 11, 21, 25, 31, 38
B. You add $2 to a piggy bank and add triple the money you added the previous day for one month
C. 3, 9, 27, 81, 243
D. You start at an elevation of 12,000 feet and climb down 1,000 feet per day
E. 20, 14, 8, 2, -4, -10

Answer 1

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Let's analyze each option:

A. **1, 11, 21, 25, 31, 38**
- The differences are: 10, 10, 4, 6, 7 (not constant)
- **Not an arithmetic sequence**

B. **You add $2 to a piggy bank and add triple the money you added the previous day for one month**
- This sequence does not have a constant difference; it is a geometric growth pattern.
- **Not an arithmetic sequence**

C. **3, 9, 27, 81, 243**
- The differences are not constant, and the pattern is geometric (each term is multiplied by 3).
- **Not an arithmetic sequence**

D. **You start at an elevation of 12,000 feet and climb down 1,000 feet per day**
- The sequence would be: 12000, 11000, 10000, 9000, ..., which has a constant difference of -1000.
- **Is an arithmetic sequence**

E. **20, 14, 8, 2, -4, -10**
- The differences are: -6, -6, -6, -6, -6 (constant difference of -6).
- **Is an arithmetic sequence**

Thus, the examples of an arithmetic sequence from the options given are:

**D. You start at an elevation of 12,000 feet and climb down 1,000 feet per day**
**E. 20, 14, 8, 2, -4, -10**