Nth Term Calculator

The Nth Term Calculator allows users to determine the nth term and the sequence formula for both arithmetic and geometric sequences, as well as calculate the sum to the nth term, based on the inputs of the first term, common difference, position, and sequence type.

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How to Use the Nth Term Calculator

The Nth Term Calculator is a versatile tool designed to help you determine terms in both arithmetic and geometric sequences, find specific formulas, and calculate sums. Follow the steps below for a complete guide to using the calculator effectively.

Step 1: Enter the First Term (a₁)

  • Locate the input field labeled First Term (a₁).
  • Enter the value of the first term of your sequence. This field is required, so ensure that the number you input is accurate.

Step 2: Input the Common Difference (d) or Common Ratio

  • Find the field labeled Common Difference (d).
  • Input the common difference for an arithmetic sequence or the common ratio for a geometric sequence. This is a crucial value required to proceed.

Step 3: Specify the Position (n) of the Term

  • Enter the desired position in the sequence by using the Position (n) field.
  • The position value should be a positive integer (i.e., 1, 2, 3, …). Enter it carefully, as it is essential for calculating the nth term and other related outputs.

Step 4: Select the Sequence Type

  • Use the Sequence Type dropdown to choose the type of sequence you are working with:
    • Arithmetic Sequence – where the difference between consecutive terms is constant.
    • Geometric Sequence – where each term after the first is found by multiplying the previous term by a fixed, non-zero number.

Step 5: View the Results

  • Once all required inputs are entered, the calculator will automatically compute and display the following results:
    • Nth Term: This value represents the term at position ‘n’ in the sequence. It is calculated using the formula for either arithmetic or geometric sequences.
    • Sequence Formula: This will display the general formula used for your sequence type, incorporating your input values.
    • Sum to Nth Term: If applicable, this will display the sum of the sequence up to the specified nth term.

Ensure that you review all input values and results carefully to avoid any errors. This Nth Term Calculator aims to provide precise calculations for both arithmetic and geometric sequences, supporting educational and practical needs.