Triangular Number Worksheet/Game

Triangular Number Worksheet/Game
Welcome to Triangular Number Worksheet/Game. This game requires you to fill in the missing term in a Triangular Number Sequence. You need to identify a sequence that grows by an increasing amount each time. Scroll down the page for a more detailed explanation.

 

 

How to play the Triangular Number Game

1. The Core Objective
   You are presented with a series of four numbers. One of these numbers is missing and replaced by an input box. You must calculate the missing “Triangle Number” to move to the next level.
   

2. How the Sequence Grows
   Unlike a standard sequence where you add the same number every time, Triangle Numbers add a larger amount with every step.
   To get from the 1st to the 2nd number, you add 2.
   To get from the 2nd to the 3rd number, you add 3.
   To get from the 3rd to the 4th number, you add 4.
   The Pattern: \(1 \xrightarrow{+2} 3 \xrightarrow{+3} 6 \xrightarrow{+4} 10 \xrightarrow{+5} 15 \dots\)
   

3. Step-by-Step Gameplay
   Look at the visible neighbors: Find two numbers next to each other. Subtract the smaller one from the larger one to see what the “jump” was.
   Example: if you see 10 → 15, the jump is 5.
   Predict the next jump: If the previous jump was 5, the next jump will be 6. If the jump before that was the gap, the jump must have been 4.
   Fill the Gap: Type your calculated number into the amber box.
   Verify: Click the Verify button or press Enter.
   Correct: The box turns green, you hear a high note, and your score increases.
   Wrong: The box turns red, you hear a low buzz, and you can try again.
   

4. Strategy
   ExampleSuppose the screen shows:21 → 28 → [ ? ] → 45
   Step 1: Check the first jump. 28 - 21 = 7.
   Step 2: Since the last jump was 7, the next jump must be 8.
   Step 3: Add 8 to the last known number: 28 + 8 = 36.
   Step 4: Double-check! If the answer is 36, the next jump should be 9. 36 + 9 = 45. It matches.
   

5. Controls
   Enter Key: Quick-submit your answer.
   Skip Button: If the numbers get too high or you get stuck, click Skip to generate a brand-new, easier sequence.
   

Triangular Numbers

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