Arithmetic Sequence Calculator
Compute the nth term and sum of an arithmetic sequence.
Input Data
A1
D
N
Results
The nth term.
29
Sum of the first n terms.
155
Explanatory note about the result.
a_10=29；S_10=155
At a glance:a_n = a1 + (n−1)d; S_n = n(a1 + a_n)/2 = n(2a1 + (n−1)d)/2. Complements arithmetic-sequence and sequence calculators.
Formula
a_n = a1 + (n−1)d.
S_n = n(a1 + a_n)/2.
How to Use
- Enter a1, d and n.
- The tool returns the nth term and sum.
Case Studies
a1=2, d=3, n=5
a5 = 2+4·3 = 14; S5 = 5(2+14)/2 = 40.
FAQ
How is sum derived?
Pair terms from both ends; each pair sums to a1+a_n, and there are n/2 pairs.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.