Sequence Connections
Case 1 of 4 · Jordan R. · 1A
Build the rule. Step back once. Find where the linear function begins. Sequence terms use n = 1, 2, 3, … . The value at n = 0 belongs to the extended linear function.
Learning objectives
- I can identify the first term and common difference of an arithmetic sequence.
- I can write recursive and explicit rules.
- I can connect common difference to slope.
- I can step backward to find the value at zero.
- I can distinguish a discrete sequence from its extended linear function.
Round 1 of 3
Build forward
7, 10, 13, 16, …
The sequence begins at term 1.
| Term number n | Term value aₙ |
|---|---|
| 1 | 7 |
| 2 | 10 |
| 3 | 13 |
| 4 | 16 |
Only the marked points are part of the graph (not connected).
1 · Enter the first term
What is the first term a₁?
2 · Determine the common difference
What is the common difference d?
3 · Complete the recursive rule
Recursive: use the previous term. Enter the starting term and the change.
4 · Complete the explicit rule
Explicit: jump to any term. Use a₁ and the (n − 1) steps from term 1.
5 · Find f(0) by stepping backward
The sequence starts at n = 1. Extend it as a linear function f and step back one term to n = 0. What is f(0)?
6 · Which rule does not belong?
Two rules represent the given sequence. Choose the one that does not. Test the first term and the change between terms.