Sequence Showdown Answer Key
Sequence Showdown
Arithmetic & Geometric: Recursive & Explicit
Teacher Answer Key
This key identifies the correct mathematical solutions and the corresponding coloring codes for the "Sequence Showdown" activity.
| # | Problem Context | Mathematical Answer | Color Code |
|---|
| 1 | Sequence Type: \(-12, -7, -2, 3, ...\) | Arithmetic | |
| Red | | | |
|
| 2 | Sequence Type: \(2, -6, 18, -54, ...\) | Geometric |
Orange
|
| 3 | Common Ratio/Diff: \(600, 300, 150, 75, ...\) | \(r = 1/2\) |
DK Green
|
| 4 | Common Ratio/Diff: \(40, 33, 26, 19, ...\) | \(d = -7\) |
LT Blue
|
| 5 | Identify \(a_4\): \(-50, -40, -30, -20, ...\) | -20 |
Black
|
| 6 | Find \(a_3\): \(a_n = 3 \cdot a_{n-1}\) and \(a_1 = 4\) | 36 |
DK Blue
|
| 7 | Find \(a_5\): \(a_n = a_{n-1} + (-5)\) and \(a_1 = 20\) | 0 |
LT Green
|
| 8 | Recursive Rule: \(40, 20, 10, 5, ...\) | \(a_n = 1/2 \cdot a_{n-1}; a_1 = 40\) |
Grey
|
| 9 | Explicit Rule: \(6, 18, 54, 162, ...\) | \(a_n = 6 \cdot 3^{n-1}\) |
Purple
|
| 10 | Explicit Rule: \(50, 42, 34, 26, ...\) | \(a_n = 50 + (n-1)(-8)\) |
Orange
|
| 11 | Find \(a_{25}\): \(a_n = 5n - 15\) | 110 |
LT Blue
|
| 12 | Find \(a_5\): \(a_n = -2 \cdot 5^{n-1}\) | -1250 |
DK Blue
|
| 13 | Find \(a_{40}\): \(-2, 4, 10, 16, ...\) | 232 |
DK Blue
|
| 14 | Find \(a_{11}\): \(5, -10, 20, -40, ...\) | 5120 |
Purple
|
| 15 | Library rows: \(a_1=30, d=4\). Find \(a_{12}\). | 74 | Solution: \(30 + (11)(4)\) |
Arithmetic
- Recursive: \(a_n = a_{n-1} + d\)
- Explicit: \(a_n = a_1 + (n-1)d\)
- Linear Form: \(a_n = dn + a_0\)
Geometric
- Recursive: \(a_n = a_{n-1} \cdot r\)
- Explicit: \(a_n = a_1 \cdot r^{n-1}\)
- Exponential Form: \(f(n) = a \cdot b^x\)
