Quadratic Sequence Worksheet/Game

Quadratic Sequence Worksheet/Game
Welcome to Quadratic Sequence Worksheet/Game. This game requires you to identify the algebraic formula an² + bn + c for a quadratic sequence. Scroll down the page for a more detailed explanation.

 

 

How to play the Quadratic Sequence Game

1. The Objective
   At the top of the screen, you are given a Target Data Stream (a sequence of 5 numbers). These numbers were created using a quadratic formula:
   an² + bn + c (Where n is the position of the number in the sequence: 1, 2, 3, 4, and 5).
   Your job is to find the correct values for the coefficients a, b, and c.
   

2. How to Calibrate
   In the center of the screen, you have the Formula Calibrator with three dials:
   Coefficient a:
   This multiplier affects the n² part of the formula. It controls how fast the sequence curves or grows.
   Coefficient b:
   This multiplier affects the n part. It shifts the sequence linearly.
   Constant c:
   This is the “offset.” It moves the entire sequence up or down by a fixed amount.
   Use the [ + ] and [ - ] buttons to change these values.
   

How to find the formula for a quadratic sequence:
Finding the formula an² + bn + c works in three steps:

1. Find a: Subtract the terms twice. The “second difference” is always equal to 2a. If the second difference is 1, then a = 0.5.
   

2. Find b: The difference between the first and second term (n₁ and n₂) is equal to 3a + b. Plug in your a to solve for b.
   

3. Find c: The first term (n₁) is always equal to a + b + c. Plug in your a and b to solve for c.
   

4. Real-Time Feedback
   As you adjust the dials, look at the Current Output Stream at the bottom:This shows the numbers generated by your current formula.
   Green Blocks: These mean your number perfectly matches the target number for that position.
   Grey Blocks: These mean your current formula is still incorrect for that position.
   

5. Verification and Streaks
   Once all 5 blocks in your Output Stream turn green and match the Target Stream, click Verify Sequence Calibration.
   Success: The screen turns green, your formula is verified, and your Clearance Streak increases. A new round will begin.
   Error: If you submit an incorrect formula, the screen will shake, and your streak will reset to zero and you need to try again.
   

Formula for Quadratic Sequence

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