Sequence Calculator

The Sequence Calculator allows users to compute the nth term and sum of terms for both arithmetic and geometric sequences by inputting the first term, sequence type, common difference or ratio, and the number of terms.

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How to Use the Sequence Calculator

This guide will take you through the steps required to effectively use the Sequence Calculator to determine specific properties of arithmetic and geometric sequences. Follow each step carefully to ensure accurate results.

Step 1: Enter the First Term

  • Locate the input field labeled First Term (a₁).
  • Enter the first term of your sequence into this field. Ensure that the number is between -1,000,000 and 1,000,000 as per the validation constraints.

Step 2: Select the Sequence Type

  • Identify the field labeled Sequence Type.
  • Choose the type of sequence you are working with. You have two options:
    • Arithmetic Sequence
    • Geometric Sequence

Step 3: Enter the Common Difference or Ratio

  • Look for the input labeled Common Difference/Ratio.
  • Input the common difference for an arithmetic sequence or the common ratio for a geometric sequence. The value should lie within the range of -1,000,000 and 1,000,000.

Step 4: Specify the Number of Terms

  • Find the field labeled Number of Terms (n).
  • Enter the total number of terms you wish to calculate. The permissible range for this field is from 1 to 100. Ensure the input is a positive integer due to the step validation of 1.

Step 5: Review the Results

After populating all the fields, the calculator will provide you with the results based on your inputs. The results include:

  • nth Term: This field will display the calculated nth term of the sequence, formatted to two decimal places.
  • Sum of Terms: The total sum of the sequence terms will be shown here, also rounded to two decimal places. Note that the calculation depends on the type of sequence you selected:
    • For an arithmetic sequence, the sum is calculated using the formula: (n * (2a₁ + (n – 1) * d)) / 2.
    • In a geometric sequence, the sum is derived from: a₁ * (rn – 1) / (r – 1).

By following these steps, you will be able to utilize the Sequence Calculator effectively for both arithmetic and geometric sequences. Double-check your inputs to ensure they fall within the required validation criteria for accurate results.