Track quiz
Keep this table beside you. Read the quantity a question names. Then use the rule that finds it.
| Idea | How it goes |
|---|---|
| The fold | Pair the ends inward; every end pair totals a + l. |
| The total | Sₙ = n/2 (a + l); the middle counts once. |
| The other face | Sₙ = n/2 (2a + (n − 1)d) — from a and d alone. |
| Backwards | With a and d known, unknown n gives a quadratic. That needs d not 0. Keep only a whole count of terms, at least 1. Unknown d: linear. |
| Terms from sums | a₁ = S₁, since nothing comes before the first term. Then aₙ = Sₙ − Sₙ₋₁ for n = 2, 3, 4, and so on. |
| Two sums | Two totals, for different counts of terms, give two linear equations. |
| Stories | Say what is given and what is missing. The story can show that an answer is wrong. |
| Is it a term | Put the number in aₙ = a + (n − 1)d. A term needs n to be a whole number, at least 1. |
| Two facts | Write each fact as a + (n − 1)d. Subtract to get d. Then find a. |
On 6, 11, 16, 21, 26, why is every end pair 32?
An AP has a = 4 and d = 3. What is its total for 30 terms?
A 12-term list starts at 5 and its last term is 60. What is its total?
How many terms of 2, 8, 14, … add up to 290?
How many terms of 30, 26, 22, … add up to 126?
A list's total is Sₙ = 3n² + 2n. What is the list?
A list has S₄ = 28 and S₆ = 54. Which list is it?
A log pile has 18 logs at the bottom, 1 on top. Each row up has one fewer. How many logs?
A cyclist rides 40 km on day one. Each day after is 5 km less. What do 8 days cover? When does the ride reach 0 km?
Which question needs you to solve for n?
Which term of 9, 16, 23, 30, … is 107?
The 3rd term of a list is 9. The 5th term is 15. What is d?
Chapter 5 of your Mathematics book is Arithmetic Progressions. You could name a term. Now you can total a whole list too.
Next: Triangles — shapes whose sides scale by one number, angles unchanged.