Question

Match each vocabulary word with the correct definition. The vocabulary words are arithmetic sequence, Sigma notation, Formula to find the sum of a finite geometric series, Geometric series, infinite sequence, common ratio (in sequences), geometric sequence, sequence, series, and common difference. The correct definitions are: An ordered list of numbers. Example: 4, 8, 12, 16, A sequence that never ends. Example: 5, 10, 20, 40, A sequence (such as 1, 3, 5) in which the difference between a term and its predecessor is always the same, The sum of sequence terms. Example:2+6+18+54, n/n=1 ar^(n-1), The difference between two consecutive terms of an arithmetic sequence, A series (such as 1+x+x2+x3) whose terms form a geometric progression, Sn=a 1-r^n/1-r, The number you multiply by each time to get the next term in a geometric sequence, A sequence where the numbers are multiplied by the same number each time. Example: 2, 6, 18, 54.

Answer 1

- sequence — An ordered list of numbers. Example: 4, 8, 12, 16
- infinite sequence — A sequence that never ends. Example: 5, 10, 20, 40
- arithmetic sequence — A sequence (such as 1, 3, 5) in which the difference between a term and its predecessor is always the same
- series — The sum of sequence terms. Example: 2+6+18+54
- Sigma notation — Σ_{n=1} a r^{n-1} (written in the prompt as "n/n=1 ar^(n-1)")
- common difference — The difference between two consecutive terms of an arithmetic sequence
- geometric series — A series (such as 1 + x + x^2 + x^3) whose terms form a geometric progression
- Formula to find the sum of a finite geometric series — S_n = a(1 − r^n)/(1 − r) (written in the prompt as "Sn=a 1-r^n/1-r")
- common ratio (in sequences) — The number you multiply by each time to get the next term in a geometric sequence
- geometric sequence — A sequence where the numbers are multiplied by the same number each time. Example: 2, 6, 18, 54