Explicit Formula Calculator

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Explicit Formula Calculator

An explicit formula provides a direct way to find any term in a sequence or the value of a function without needing to know the preceding terms. This calculator allows you to input an explicit mathematical formula and a specific value for the variable 'n' (or 'x'), then computes the result.

How to Use This Calculator:

  1. Enter Your Formula: Type your mathematical formula into the "Formula" field. Use 'n' as your variable.
  2. Use Standard Operators:
    • Addition: +
    • Subtraction: -
    • Multiplication: * (e.g., 2*n, not 2n)
    • Division: /
    • Parentheses: () for grouping
    • Exponents: Use Math.pow(base, exponent) (e.g., Math.pow(n, 2) for n squared, or Math.pow(2, n) for 2 to the power of n).
    • Other Math Functions: You can use standard JavaScript Math object functions like Math.sqrt(), Math.sin(), Math.cos(), Math.log(), etc.
  3. Enter 'n' Value: Input the numerical value for 'n' at which you want to evaluate the formula.
  4. Calculate: Click the "Calculate" button to see the result.

Examples of Explicit Formulas:

  • Arithmetic Sequence: For a sequence like 5, 8, 11, 14… the explicit formula is 3*n + 2 (where n starts from 1).
  • Geometric Sequence: For a sequence like 3, 6, 12, 24… the explicit formula is 3 * Math.pow(2, n-1) (where n starts from 1).
  • Quadratic Function: Math.pow(n, 2) + 2*n + 1
  • More Complex: (Math.pow((1+Math.sqrt(5))/2, n) - Math.pow((1-Math.sqrt(5))/2, n)) / Math.sqrt(5) (Binet's formula for Fibonacci numbers, where n starts from 1).

Result:

function calculateExplicitFormula() { var formulaString = document.getElementById("formulaInput").value; var nValue = parseFloat(document.getElementById("nValue").value); var resultDiv = document.getElementById("result"); if (formulaString.trim() === "") { resultDiv.innerHTML = "Please enter a formula."; return; } if (isNaN(nValue)) { resultDiv.innerHTML = "Please enter a valid number for 'n'."; return; } // Replace 'n' with the actual value in the formula string // Use a regex with global flag to replace all occurrences var evaluatedFormula = formulaString.replace(/n/g, nValue); try { // Use a function constructor for safer evaluation than direct eval() // This creates a function that takes 'n' as an argument and returns the result // It still uses eval-like capabilities internally, but within a more controlled scope. // For this specific use case (mathematical expressions on a user's own site), it's generally acceptable. var calculateFunction = new Function('n', 'return ' + formulaString + ';'); var calculatedResult = calculateFunction(nValue); if (isNaN(calculatedResult)) { resultDiv.innerHTML = "Error: The formula resulted in an invalid number. Check your syntax."; } else { resultDiv.innerHTML = "The value of the formula at n = " + nValue + " is: " + calculatedResult + ""; } } catch (e) { resultDiv.innerHTML = "Error evaluating formula: " + e.message + ". Please check your formula syntax."; } } .explicit-formula-calculator { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; max-width: 700px; margin: 20px auto; padding: 25px; background: #f9f9f9; border-radius: 10px; box-shadow: 0 4px 12px rgba(0, 0, 0, 0.1); border: 1px solid #e0e0e0; } .explicit-formula-calculator h2 { color: #333; text-align: center; margin-bottom: 20px; font-size: 28px; } .explicit-formula-calculator h3 { color: #555; margin-top: 20px; margin-bottom: 10px; font-size: 20px; } .explicit-formula-calculator p, .explicit-formula-calculator ol, .explicit-formula-calculator ul { color: #666; line-height: 1.6; margin-bottom: 10px; } .explicit-formula-calculator ol li, .explicit-formula-calculator ul li { margin-bottom: 5px; } .explicit-formula-calculator .calculator-form { background: #ffffff; padding: 20px; border-radius: 8px; border: 1px solid #e5e5e5; margin-top: 20px; } .explicit-formula-calculator label { display: block; margin-bottom: 8px; color: #333; font-weight: bold; } .explicit-formula-calculator input[type="text"], .explicit-formula-calculator input[type="number"] { width: calc(100% – 22px); padding: 10px; margin-bottom: 15px; border: 1px solid #ccc; border-radius: 5px; font-size: 16px; } .explicit-formula-calculator button { background-color: #007bff; color: white; padding: 12px 25px; border: none; border-radius: 5px; cursor: pointer; font-size: 18px; display: block; width: 100%; transition: background-color 0.3s ease; } .explicit-formula-calculator button:hover { background-color: #0056b3; } .explicit-formula-calculator .result-container { margin-top: 25px; padding: 15px; background-color: #e9f7ef; border: 1px solid #d4edda; border-radius: 8px; text-align: center; } .explicit-formula-calculator .result-container h3 { color: #28a745; margin-top: 0; font-size: 22px; } .explicit-formula-calculator .result-container p { font-size: 24px; color: #333; font-weight: bold; margin: 0; } .explicit-formula-calculator .result-container p strong { color: #0056b3; }

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