Formula and example
How it is calculated
Arithmetic: aₙ=a₁+(n−1)d, Sₙ=n(a₁+aₙ)/2. Geometric: aₙ=a₁q^(n−1), Sₙ=a₁(1−qⁿ)/(1−q) for q≠1.
Worked example
The arithmetic sequence 3, 5, 7, 9, 11 has fifth term 11 and a sum of 35.
Things to check
- n must be a positive integer. Geometric sequences may also use a negative or zero ratio.
- For q=1, the geometric sequence is constant and its sum is n·a₁. Powers beyond the representable number range are rejected.
Frequently asked questions
Why is the exponent n−1?
The first term is already a₁. Reaching the second term requires one multiplication; reaching the nth term requires n−1 multiplications by the ratio.