Is the the sequence #5a-1, 3a-1, a-2, -a-1,...# arithmetic?

1 Answer
Noah G
Dec 11, 2016

Interpretation 1: Assuming the question is with #a- 2#:

The common difference, #d#, of a sequence will determine whether it is arithmetic, geometric or neither. If it is arithmetic, the common difference will be a common number added or subtracted from the previous term.

#d = t_2 - t_1#

#d = 3a - 1 - (5a - 1)#

#d = 3a - 1 - 5a + 1#

#d = -2a#

#d= t_3 - t_2#

#d = a - 2 - (3a - 1)#

#d = -2a - 1#

Since the two numbers aren't the same, this sequence is not arithmetic

Interpretation 2: Assuming the question is with #a - 1#

Doing the same process as above:

#d = t_2 - t_1#

#d = 3a - 1 - (5a - 1)#

#d = 3a - 1 - 5a + 1#

#d = -2a#

#d = t_3 - t_2#

#d = a - 1 -(3a - 1)#

#d = a - 1 - 3a + 1#

#d = -2a#

Since the two #d's# are the same, this sequence is arithmetic.

Hopefully this helps!

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