Find the Nth Term Formula Calculator

Sequence Formula:

\[ a_n = a_1 + (n-1)d \] (for arithmetic sequences)
\[ a_n = a_1 \times r^{(n-1)} \] (for geometric sequences)

Nth Term Formula:

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1. What is the Nth Term Formula?

The nth term formula allows you to find any term in a sequence without listing all previous terms. For arithmetic sequences, each term increases by a constant difference. For geometric sequences, each term is multiplied by a constant ratio.

2. How Does the Calculator Work?

The calculator uses standard sequence formulas:

Arithmetic: \[ a_n = a_1 + (n-1)d \]
Geometric: \[ a_n = a_1 \times r^{(n-1)} \]

Where:

\( a_n \) — nth term of the sequence
\( a_1 \) — first term of the sequence
\( d \) — common difference (arithmetic)
\( r \) — common ratio (geometric)
\( n \) — term position

Explanation: The formula calculates any term directly based on its position in the sequence.

3. Importance of Sequence Formulas

Details: Sequence formulas are fundamental in mathematics, used in financial calculations, computer algorithms, physics, and engineering problems involving patterns.

4. Using the Calculator

Tips: Select sequence type, enter first term and common difference/ratio. The calculator will generate the general formula for the nth term.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between arithmetic and geometric sequences?
A: Arithmetic adds a constant difference each step, while geometric multiplies by a constant ratio.

Q2: Can this calculator handle quadratic sequences?
A: No, this calculator only handles simple arithmetic and geometric sequences.

Q3: How do I find the common difference in a sequence?
A: Subtract any term from the term that follows it (for arithmetic sequences).

Q4: What if my sequence isn't arithmetic or geometric?
A: More complex sequences require different approaches like finite differences or pattern recognition.

Q5: Can I use this for recursive sequences?
A: No, recursive sequences define terms based on previous terms rather than position.