Which of the following are arithmetic sequences?

Which of the following are arithmetic sequences?

A) 1, 2, 3, 4, 5, 6…

B) 2, 6, 18, 54…

C) 100, 230, 360, 490

D) 2, 2, 2, 2, 2…

Answer: The correct options are A and D.

According to the definition, an arithmetic sequence is a sequence of numbers in which the difference between the consecutive terms is the same. This common difference is the constant by which the second term is to be added or subtracted from the first term to obtain the next term.

A) one, two, three, four, five, six. .. is an arithmetic sequence having the common difference of 1. Sequence B is 2, 6, 18, 54. .. has nothing to do with arithmetic sequences since sequence a is a geometric sequence. C) 100, 230, 360, 490 is not an arithmetic sequence as the difference is not a constant, also it’s not a geometric sequence as the ratio is not constant. Answer D) 2, 2, 2, 2, 2. .. is an arithmetic sequence whose common difference is 0.

Arithmetic sequences may be of positive sign, negative sign or zero for the common difference, but in the geometric sequences, the common ratio is used, instead of the common difference.