Arithmetic Sequence Calculator
Compute the nth term and sum of an arithmetic sequence.
Input Data
First Term
Common Difference
Term Count
Results
The Nth term.
19
Sum of the first N terms.
100
At a glance:a_N = a1 + (N−1)d; S_N = N·(a1 + a_N)/2. Complements arithmetic-seq and sequence calculators.
Formula
a_N = a1 + (N−1)d.
S_N = N(a1 + a_N)/2.
$$a_n = a_1 + (n-1)d$$$$S_n = \frac{n}{2}(a_1 + a_n) = \frac{n}{2}[2a_1 + (n-1)d]$$How to Use
- Enter first term, difference and N.
- The tool returns the Nth term and sum.
Case Studies
a1=1, d=2, N=4
a4 = 1+3·2 = 7; S4 = 4(1+7)/2 = 16.
FAQ
What if difference is negative?
The sequence decreases; formulas still apply with negative d.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.