Term of Quadratic Sequence Worksheet/Game

Next Term of Quadratic Sequence Worksheet/Game
Welcome to Next Term of Quadratic Sequence Worksheet/Game. This game requires you to find the first differences and the second difference and use that to find the next term in the quadratic sequence. Scroll down the page for a more detailed explanation.

 

 

How to play the Quadratic Sequence Game

1. The Objective
   The game presents you with the first four terms of a sequence. Your goal is to calculate and enter the 5th term into the input box.
   

2. How to Play
   Step 1. Analyze the Pattern: Look at the four numbers provided in the white cards.
   Step 2. Calculate the Differences: Find the “jump” between each number.
   Step 3. Enter your guess: Type the next number into the large input box and click “Check Prediction” or press Enter.
   Step 4. Advance: If you are correct, click “Next Sequence” to start a new round and build your streak. If you are wrong, your streak resets to 0.
   

3. The Math Strategy
   Because these are Quadratic Sequences, the difference between the numbers changes at a steady rate. To find the 5th term without an advanced formula, use the Method of Differences:
   

Step-by-Step
Example: Suppose the game gives you: 2, 6, 12, 20
Step A: Find the First Differences
6 - 2 = 4
12 - 6 = 6
20 - 12 = 8
(The differences are 4, 6, 8… they aren’t the same, so it’s quadratic)
Step B: Find the Second Difference
6 - 4 = 2
8 - 6 = 2 (The “jump” between the differences is a constant 2.)
Step C: Predict the Next “Jump”
Take the last jump (8) and add the constant second difference (2).
8 + 2 = 10
Step D: Find the 5th Term
Add that new jump (10) to the last term you saw (20).
20 + 10 = 30
Your answer would be 30.

4. Game Controls
   Input Box: Where you type your prediction.
   Check Prediction: Submits your answer for verification.
   Correct/Streak: Tracks your total wins and your current consecutive wins.
   Next Sequence: Randomly generates a brand new quadratic pattern for you to solve.
   

Next term for Quadratic Sequence

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