- Sequence
- 2, 5, 8, 11, 14, 17, 20, 23, 26, 29
- Sum
- 155
Detailed breakdown
| Term | Value |
|---|---|
| 1 | 2 |
| 2 | 5 |
| 3 | 8 |
| 4 | 11 |
| 5 | 14 |
| 6 | 17 |
| 7 | 20 |
| 8 | 23 |
| 9 | 26 |
| 10 | 29 |
How it works
A term and a sum answer differently
For 2,5,8,11, the fourth term is 11 but the sum of four terms is 26. Use the term to identify a position and the sum to describe accumulated quantity across those positions.
Identifying the sequence model before extending it
A sequence calculator can extend only the pattern described by the selected model and inputs. Several different rules can fit a short list of terms, so an apparent pattern is not proof of a unique continuation. Distinguish the value of a particular term from the sum of several terms. Check the starting index and common difference or ratio when comparing results.
Sequence: formula and assumptions
Arithmetic: aₙ = a₁ + (n−1)d. Geometric: aₙ = a₁r^(n−1). Fibonacci: aₙ = aₙ₋₁ + aₙ₋₂.
Fibonacci starts with 0 and 1 and ignores the first-term and difference inputs.
Nth term and series sum: formula and assumptions
Arithmetic: aₙ=a₁+(n−1)d. Geometric: aₙ=a₁r^(n−1). Fibonacci uses F₀=0, F₁=1.
The Fibonacci result uses exact integers through index 10,000. Arithmetic and geometric sequences begin at index one.
Worked example
Using the Sequence example:
- Sequence type
- arithmetic
- First term
- 2
- Difference or ratio
- 3
- Number of terms
- 10
Arithmetic: aₙ = a₁ + (n−1)d. Geometric: aₙ = a₁r^(n−1). Fibonacci: aₙ = aₙ₋₁ + aₙ₋₂.
Example result
Sequence: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29
Sum: 155
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
Does the first term always have index one?
Arithmetic and geometric sequences start at index one. Fibonacci uses F0 = 0 and F1 = 1.
Do first-term and difference inputs change the Fibonacci sequence?
No. Fibonacci uses its fixed starting values and recurrence. Those controls apply to the other sequence types.
Prepared by Finflo. See our methodology and editorial policy.