Geometric Series Calculator

Find aₙ and Sₙ of a Geometric Series with Step-by-Step Solutions

Calculate the nth term and the sum of the first n terms of a geometric sequence.

Formulas

For a geometric sequence with first term \( A_1 \) and common ratio \( r \):

\[ \text{nth term: } a_n = A_1 \cdot r^{n-1} \] \[ \text{Sum of first n terms: } S_n = A_1 \cdot \frac{1 - r^n}{1 - r} \quad (r \neq 1) \]

\( A_1 \) (first term)

\( r \) (common ratio)

\( n \) (number of terms)

\( A_1 \) and \( r \) accept decimals or fractions (e.g., 2.1, 3/4, -2/3). \( n \) must be a positive integer.

\( a_n \) (nth term)

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\( S_n \) (sum of first n terms)

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Enter values and click "Calculate"

Step-by-step solution will appear here after calculation.

\( a_n = A_1 \cdot r^{n-1} \) | \( S_n = A_1 \cdot \frac{1 - r^n}{1 - r} \)