nth Term Worksheet/Game

nth Term Worksheet/Game
Welcome to nth Term Worksheet/Game. This game requires you to translate a visual sequence into a mathematical expression (nth term) and then use that expression to find any term. Scroll down the page for a more detailed explanation.

 

 

How to play the nth Term Game
Phase 1: The Rule Hunt
When the game starts, you will see four cards labeled n₁ through n_4. Your goal is to find the Algebraic Rule (dn + c).

1. Find the Difference (d): Look at how much the value changes between each card. If n₁ = 10 and n₂ = 13, the difference is 3. This becomes the number in front of n (e.g., 3n).
   
2. Find the Adjustment (c): Calculate what 3 × n would be for the first card. For n₁, 3 × 1 = 3. Since the card value is 10, you need to add 7 to get there.
   
3. Enter the Rule: In the input box, type your formula (e.g., 3n+7).
   

Phase 2: Calculate the term
Once you verify the rule, the game moves to Step 2: Solve for n.

1. Review the Formula: Your correct rule will be displayed in a box at the top (e.g., 3n + 7).
   
2. Find the Target: The game will ask you for a specific distant term, like n₅₀ or n₁₀₀.
   
3. Calculate: Plug that number into your formula.
   Example: If the rule is 3n+7 and you need to find n₁₀₀:
   (3 × 100) + 7 = 307.
   
4. Submit: Type the result into the box and hit Enter or click Solve.
   

Winning and Losing
The Streak: Every time you successfully complete both phases, your Logic Streak increases.
The Reset: If you enter an incorrect formula in Phase 1 or a wrong calculation in Phase 2, the “Logic Processing Unit” fails, your streak resets to 0, and a brand-new sequence is generated.
Next Challenge: After a success, click the Next Challenge button to generate a harder sequence (which may include negative numbers).

Tip:
If the numbers are decreasing, your d value will be negative (e.g., -5n + 20). Always check your rule against the second or third card before submitting.

nth Term of an Arithmetic Sequence

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