How to Use the Arithmetic & Geometric Sequence Calculator
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1
Select sequence type: Arithmetic Progression (AP) or Geometric Progression (GP).
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2
Enter the first term $a_1$ and common difference $d$ (for AP) or common ratio $r$ (for GP).
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3
Enter the target term number $n$ (e.g. $n = 20$).
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4
The calculator computes the $n$-th term $a_n$ and the sum of the first $n$ terms $S_n$.
Practical Example & Use Case
Common Real-World Scenario
For an arithmetic sequence starting at 5 with difference 3, the 50th term is $a_{50} = 5 + (49 \times 3) = 152$ and the sum of 50 terms is $3,925$.
Technical Notes & Limitations
Browser Engine Architecture
Calculates infinite geometric series sum $S_\infty = \frac{a}{1-r}$ when $|r| < 1$.
Frequently Asked Questions
What is the sum formula for an arithmetic sequence?
$S_n = \frac{n}{2}(2a_1 + (n-1)d) = \frac{n}{2}(a_1 + a_n)$.