Geometric Sequence Calculator
Geometric sequence calculator
Compute nth term and finite-series sum for geometric progressions.
Result
a8 = 51.2578125
Sum of first 8 terms = 147.7734375.
Auto
math
Flow
- Enter first term, common ratio, and term index.
- Read nth term and cumulative finite sum.
- Use ratio near 1 carefully for sensitivity checks.
Example
Worked example: a1 = 3, r = 1.5, n = 8
- 1 Compute a8 = 3 × 1.5^7.
- 2 Use finite sum formula with ratio not equal to 1.
- 3 Report nth term and total of first 8 terms.
a8 ≈ 51.2578 and S8 ≈ 145.7734.
How
- Enter first term, common ratio, and term index.
- Read nth term and cumulative finite sum.
- Use ratio near 1 carefully for sensitivity checks.
Avoid
- Using arithmetic sequence formula for multiplicative growth.
- Forgetting exponent n-1 in nth-term calculation.
Checks
Best fit
Geometric Sequence Calculator is built for calculate nth term and finite sum for geometric sequences. If Geometric Sequence Calculator does not match the input scope, compare the answer with a second method.
Input check
Match the entered values to this rule before copying the answer: an = a1 × r^(n-1), Sn = a1(1-r^n)/(1-r).
Sanity check
For Geometric Sequence Calculator, use the worked example as a quick benchmark: A8 ≈ 51.2578 and S8 ≈ 145.7734. If the geometric sequence calculator answer is far away, check whether an input, unit, or mode changed.
Before copying
Review this common issue first: using arithmetic sequence formula for multiplicative growth.
FAQ
What happens when r = 1?
All terms are equal and sum becomes a1 × n.
Can ratio be negative?
Yes. Terms alternate sign while formulas still apply.
Is this infinite-series sum?
No. This tool computes finite sum to n terms.
Switch
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