Recursive Formula Calculator

The Recursive Formula Calculator allows users to calculate and explore arithmetic, geometric, and linear sequences by inputting initial values, multipliers, constants, and specifying the number of terms.

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How to Use the Recursive Formula Calculator

This guide provides a step-by-step process to use the Recursive Formula Calculator for calculating terms in a sequence using either a linear, geometric, or arithmetic formula.

Step 1: Provide the Initial Value

Locate the field labeled Initial Value (a₁). Enter the starting value of your sequence here. Ensure that the value is between -1,000,000 and 1,000,000, as required by the validation rules.

Step 2: Enter the Multiplier

In the field labeled Multiplier (r), input the multiplier value. This value is used in both linear and geometric formulas. The permissible range for this value is -100 to 100, with steps of 0.01. Ensure the value entered adheres to these constraints.

Step 3: Specify the Constant

Next, provide a constant value in the field labeled Constant (k). This is used in both the linear and arithmetic formulas. Like the initial value, this field accepts numbers between -1,000,000 and 1,000,000.

Step 4: Select the Number of Terms

In the field labeled Calculate up to nth term, specify the number of terms you would like the calculator to compute. You can select any integer value between 1 and 20.

Step 5: Choose the Formula Type

  • Linear: Select this if your recursive formula follows the form aₙ = r·aₙ₋₁ + k.
  • Geometric: Choose this if your formula is aₙ = r·aₙ₋₁.
  • Arithmetic: Pick this option if your formula follows aₙ = aₙ₋₁ + k.

Select your formula type from the dropdown list provided under Formula Type.

Step 6: Compute the Terms and Their Sum

Once all fields are filled in correctly according to the requirements, the calculator will automatically compute the terms and display them alongside their labels such as 1st Term, 2nd Term, and so on. It will calculate up to a 5th term depending on your specified n value and will also display the sum of the terms up to your nth term.

The results for each term and the sum will be formatted and displayed with up to four decimal places for precision.

Now you are set to use the Recursive Formula Calculator effectively to compute sequences based on the parameters provided!