Track quiz
Show on a big screenKeep 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.
Reveal every answer to finish this lesson.
That is the end of this subject for Class 10
Nicely done. There is more waiting at this same level — pick whichever you like.