Activity
Jada and Mai are trying to decide what type of sequence this could be:
| term number | value |
| 1 | 2 |
| 2 | 6 |
| 5 | 18 |
Jada says: “I think this sequence is geometric because in the value column, each row is 3 times the previous row.”
Mai says: “I don’t think it is geometric. I graphed it, and it doesn’t look geometric.”
Do you agree with Jada or Mai? Be prepared to show your reasoning using a graph.
Compare your answer:
I agree with Mai. Jada noticed that each value is multiplied by 3 to get to the next row, but the table skips terms. If the sequence were geometric, it would have to be 2, 6, 18, 54, 162. When Mai made a graph, she could see the gap in the sequence.
Without knowing the missing terms, we don’t know for sure if the sequence is arithmetic, but it could be since the three given points are all on the same line with slope 4. The missing points could be and so that the sequence would be 2, 6, 10, 14, 18.
Self Check
Additional Resources
Creating a Sequence
For a sequence: 1, 3, . . .
Write the next two terms that would make the sequence
- geometric
- arithmetic
Solution
- To make the sequence geometric, there must be a common ratio. , so use a common ratio of 3 to multiply each term by. The sequence becomes: 1, 3, 9, 27 . . .
- To make the sequence arithmetic, there must be a common difference. , so use a common difference of 2 to add to each term. The sequence becomes: 1, 3, 5, 7 . . .
Try it
Try It: Creating a Sequence
Write the next two terms to create an arithmetic sequence.
2, 6, . . .
Here is how to create an arithmetic sequence given two terms:
Find the common difference by subtracting the first term from the second term:
The common difference is 4.
Add 4 to the previous term to find the next terms.
The sequence becomes: 2, 6, 10, 14 . . .