arithmetic sequence


Definition of Arithmetic Sequence

  • Arithmetic sequence is a sequence of numbers that has a constant difference between every two consecutive terms.
  • In other words, arithmetic sequence is a sequence of numbers in which each term except the first term is the result of adding the same number, called the common difference, to the preceding term.

Example of Arithmetic Sequence

  • The sequence 5, 11, 17, 23, 29, 35 . . . is an arithmetic sequence, because the same number 6 (i.e. the common difference) is added to each term of the sequence to get the succeeding term.

More about Arithmetic Sequence

  • Arithmetic series is the indicated sum of the terms of an arithmetic sequence.

Example of Arithmetic Series

  • The sequence 5, 11, 17, 23, 29, 35 is an arithmetic sequence.
  • 5 + 11 + 17 + 23 + 29 + 35 is the corresponding arithmetic series.

Solved Example on Arithmetic Sequence

Find the next four terms of the given arithmetic sequence.
7, 4, 1, - 2, - 5 . . .
Choices:
A. – 3, - 3, - 3, - 3
B. – 8, -5, -2, 1
C. – 8, - 11, - 14, - 17
D. 8, 11, 14, 17
Correct Answer: C
Solution:
Step 1: The common difference for the given sequence is – 3.
Step 2: So, the next four terms are – 8, - 11, - 14, - 17.

Related Terms for Arithmetic Sequence

  • Sequence
  • Term
  • Common Difference
  • Arithmetic Series