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💡 What Does "…" Mean?
When you see three dots … in math, they mean "keep going in the same pattern."
For example:
1, 2, 3, …, 10 means "1, 2, 3, 4, 5, 6, 7, 8, 9, 10" — all the numbers up to 10.
2, 4, 6, … means "2, 4, 6, 8, 10, 12, …" — keep going forever by 2s!
1 What Comes Next? 🔮
Figure out the pattern, then write the next three numbers.
1
2
3
4
?
?
?
Rule: add each time
2
4
6
8
?
?
?
Rule: add each time
1
3
5
7
?
?
?
Rule: add each time
5
10
15
20
?
?
?
Rule: add each time
🧩 From Pattern to Formula
A formula is a shortcut that lets you jump straight to any number in the pattern — without listing them all!
Even numbers: 2, 4, 6, 8, … → The nth even number = 2 × n.
Odd numbers: 1, 3, 5, 7, … → The nth odd number = 2 × n − 1.
2 Test the Formulas 🧪
Use the formulas to fill in the tables. Check that they match the patterns!
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🚀 Why Formulas Are Powerful
Without a formula, finding the 100th odd number means listing all of them:
1, 3, 5, 7, 9, 11, 13, … (counting 100 numbers — that takes forever!)
With the formula 2 × n − 1, you jump straight there:
2 × 100 − 1 = 200 − 1 = 199. Done! ⚡
3 Jump Ahead! 🚀
Use the formula to find the answer — no need to list them all!
The 7th even number
Formula: 2 × n
2 × 7 =
The 20th even number
Formula: 2 × n
2 × =
The 7th odd number
Formula: 2 × n − 1
2 × 7 − 1 =
The 20th odd number
Formula: 2 × n − 1
2 × − 1 =
4 Match the Formula 🎯
Each pattern below follows a formula. Write the formula using n. The first one is done for you.
| Pattern | 1st | 2nd | 3rd | 4th | 5th | Formula |
|---|
| Multiples of 3 |
3 | 6 | 9 | 12 | 15 |
3 × n |
| Multiples of 4 |
4 | 8 | 12 | 16 | 20 |
|
| Add-one pattern |
2 | 3 | 4 | 5 | 6 |
|
| Squares |
1 | 4 | 9 | 16 | 25 |
|
5 Formula Word Problems 🌍
Use each formula to solve the real-world problem.
Bus seats = 4 × rows
If rows = 8:
4 × =
Postage = 2 × stamps (¢)
If stamps = 15:
2 × =
Cousin's age = n + 3
If n = 9:
+ 3 =
Savings = 5 × weeks
If weeks = 12:
5 × =
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6 Say It in Words 💬
Write what each formula does in plain English. The first one is done for you.
n + 10
"Add 10 to the number."
2 × n
Your words:
n × n
Your words:
2 × n − 1
Your words:
7 Find the Big Numbers 🌟
Use the formula to find each answer without listing all the numbers.
The 50th even number
Formula: 2 × n
2 × 50 =
The 50th odd number
Formula: 2 × n − 1
2 × 50 − 1 =
The 100th even number
Formula: 2 × n
2 × =
The 100th odd number
Formula: 2 × n − 1
2 × − 1 =
8 Formula Story Problems 📖
Use the two-step formula to solve each story problem.
Flour = 2 × n + 1 cup
If n = 5 batches:
Step 1: 2 × 5 =
Step 2: + 1 =
Fare = 3 × n − 1 discount
If n = 6:
Step 1: 3 × 6 =
Step 2: − 1 =
Height = 4 × n + 2 base
If n = 7:
Step 1: 4 × 7 =
Step 2: + 2 =
Bags = 2 × n − 3 lost
If n = 10:
Step 1: 2 × 10 =
Step 2: − 3 =
Answer Key:
1) 5,6,7 (add 1); 10,12,14 (add 2); 9,11,13 (add 2); 25,30,35 (add 5) —
2) Even: 2,4,6,8,10 · Odd: 1,3,5,7,9 —
3) 14, 40, 13, 39 —
4) 4×n, n+1, n×n —
5) Bus: 32; Postage: 30¢; Cousin: 12; Savings: 60 —
6) "Double the number"; "Multiply the number by itself"; "Double the number and subtract 1" —
7) 100, 99, 200, 199 —
8) Flour: 11; Fare: 17; Tower: 30; Bags: 17