Math

Geometric Sequence Calculator

The infinite sum converges to a₁ ÷ (1 − r).

Find the nth term and sum of a geometric sequence.

Calculated Output

nth term 384

Sum of first n 765

Formula: aₙ = a₁ r^(n−1) ; Sₙ = a₁(1−rⁿ)/(1−r)

Step-by-Step Breakdown

1. Values used:

2. First term = 3

3. Common ratio = 2

4. Term number (n) = 8

6. nth term = 384

7. Sum of first n = 765

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The math behind it

nth term = a₁ × r^(n−1). Sum = a₁(1 − rⁿ) ÷ (1 − r) when r ≠ 1.

3, 6, 12, … 8th term = 384, sum = 765.

|r| < 1?

The infinite sum converges to a₁ ÷ (1 − r).