Sequences and Series Quick Reference
A more useful quick-reference sheet for arithmetic and geometric sequences and finite sums, with pattern checks and term-versus-sum reminders.
Formula highlights
Recognise the pattern first
- Equal difference -> arithmetic sequence
- Equal ratio -> geometric sequence
- Sequence lists terms; series adds them
Formula map
- Arithmetic nth term: a + (n - 1)d
- Arithmetic sum: n/2 x (first + last)
- Geometric nth term: a x r^(n - 1)
- Geometric finite sum depends on the common ratio r
Worked examples
5, 8, 11, 14 is arithmetic with difference 3.
2, 6, 18, 54 is geometric with ratio 3.
Use the nth-term rule for a single position and the sum rule for a cumulative total.
Practical reminders
- Do not confuse the tenth term with the sum of the first ten terms.
- Check whether the real process is additive or multiplicative before choosing the model.
Use the formulas in live tools.
Arithmetic Sequence nth Term Calculator
Use the Arithmetic Sequence nth Term Calculator for a quick arithmetic sequence nth term result with clear inputs and a readable answer.
Arithmetic Series Sum Calculator
Use the Arithmetic Series Sum Calculator for a quick arithmetic series sum result with clear inputs and a readable answer.
Geometric Sequence nth Term Calculator
Use the Geometric Sequence nth Term Calculator for a quick geometric sequence nth term result with clear inputs and a readable answer.
Geometric Series Sum Calculator
Use the Geometric Series Sum Calculator for a quick geometric series sum result with clear inputs and a readable answer.