arithmetic progression

IPA/ˌærɪθmetɪk prəˈɡreʃn/
IPA/ˌærɪθmetɪk prəˈɡreʃn/

arithmetic progression — 名詞

1. a set of numbers arranged in order where the difference between any two numbers

1.名詞B2
釋義

等差數列

相鄰兩項差為定值的數列

a set of numbers arranged in order where the difference between any two numbers that come one right after the other stays the same — for instance, 2, 5, 8, 11, 14 where the common difference is 3

例句

In Niran's math class, the teacher showed that 3, 6, 9, 12 is a simple arithmetic progression.

在 Niran 的數學課上，老師說明 3、6、9、12 就是一個簡單的等差數列。

illustrated with a named number sequence

The sequence 20, 15, 10, 5 forms an arithmetic progression where each term drops by five.

數列 20、15、10、5 構成一個等差數列，每一項都比前一項少五。

同義詞
  • arithmetic sequence

    exact same meaning; 'sequence' is slightly more common in modern textbooks than 'progression'

  • linear sequence

    broader term in some contexts; less precise because it can also refer to a sequence whose graph forms a straight line

文法句型

arithmetic progression + of + [number set]

用法筆記

The phrase 'common difference' refers to the fixed amount added (or subtracted) between consecutive terms. Distinguish from 'geometric progression', where terms are multiplied by a constant factor instead of added.

常見錯誤

❌The sequence 2, 4, 8, 16 is an arithmetic progression.
✅The sequence 2, 4, 8, 16 is a geometric progression, not an arithmetic one.
💡in an arithmetic progression the difference is constant (2, 4, 6, 8 adds 2 each time), whereas 2, 4, 8, 16 multiplies by 2.
❌Arithmetic progression is when you add numbers together.
✅An arithmetic progression is a list of numbers where each term is produced by adding a fixed amount to the previous term.
💡the concept describes a sequence, not the act of adding.