Geometric Progression Solver

Solve for the nth term and the sum of the first n terms of a geometric progression (GP).

Inputs

First Term (a)

-10,00,00010,00,000

Common Ratio (r)

-1,0001,000

Number of Terms (n)

1100

Calculation Results

Nth Term (a_n)

162

Sum of n Terms (S_n)

242

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Formula & Mathematical Explanation

\displaystyle a_n = a r^{n-1}, \quad S_n = a \frac{1 - r^n}{1 - r} \quad (r \neq 1)

A geometric progression is a sequence where each term after the first is found by multiplying the previous one by a constant ratio (r). The sum formula differs depending on whether r is equal to 1 or not.