Track quiz
Nine ideas, nine checks. Look at the table as often as you like.
| Idea | How it goes |
|---|---|
| A rule, not a guess | A rule must fit every join, not only the first. |
| Looking back | A recursive rule needs a first term to begin. |
| Jumping there | An explicit rule gives any term from its position. |
| The same step | An AP has tₙ = a + (n − 1)d. |
| Adding the first n | Two copies fill a rectangle n × (n + 1). |
| The same multiplier | A GP has tₙ = a × rⁿ⁻¹. |
| Stage counts | Stage n of the Sierpiński triangle has 3ⁿ triangles. |
| A tower and a count | Each size takes twice the last, plus one. |
| Does it really fit | Two rules can share three terms and part at the fourth. |
What makes a rule more than a lucky guess?
A recursive rule says "double the term before". No first term is given. What can it build?
The rule is tₙ = 3n + 2. Which position holds 137?
An AP starts at 5 and adds 3 at every step. What is its 10th term?
What is 1 + 2 + 3 + … + 100?
A GP starts at 2 with common ratio 3. What is its 5th term?
A list multiplies by 1/2 at every step, starting at 48. What does it do?
How many black triangles does stage 3 of the Sierpiński triangle have?
The list 1, 2, 4 fits two rules. One doubles. One adds 1, then 2, then 3. Which continues it?
Chapter 8 of Ganita Manjari is Predicting What Comes Next. Bring the question you could not finish.
Next: Linear Equations in Two Variables. Two rules that must both hold at once. One pair of numbers fits them both.