Find terms and sums in a geometric sequence.
Last updated: June 2026 | By Patchworkr Team
Enter the first term, the common ratio, and the term number.
A geometric sequence multiplies by the same ratio each time.
a_n = a1 x r^(n-1) and S_n = a1(1 - r^n) / (1 - r), with the r = 1 case handled separately.
Bacterial growth with a1 = 100 and r = 2.
1. Terms: 100, 200, 400, 800, 1600
2. 5th term = 1600
3. Sum of first 5 terms = 3100
Final answer: a5 = 1600, S5 = 3100
Can r be negative?
Yes. Negative ratios create alternating sequences.
What if r = 1?
Then the sequence is constant and the sum is a1 x n.
Can n be zero?
No. This calculator requires n >= 1.
Does the preview show every term?
It shows up to the first 10 terms so long sequences stay readable.
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