How do you tell whether the sequence 2, -5, -12, -19, -26# is arithmetic?

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Answer 1 · 2017-07-17T02:40:21

Yes, sequence is arithmetic.

For a sequence to be arithmetic all consecutive terms must differ by a fixed amount #(d)# called the common difference.

Thus if #a_1# in the first term, #a_2 = a_1 +d #

In general: #a_(n+1) = a_n+d -> d = a_(n+1) -a_n#

In our sequence: #2, -5, -12, -19, -26#

#a_1 = 2#

#a_2 = -5#

If the sequence is to be arithmetic: #d = -5-2 =-7#

Testing the next terms in tern:

#a_3 = -5 -7 = -12# Correct

#a_4 = -12 -7 = -19# Correct

#a_5 = -19 -7 = -26# Correct

Since all terms satisify the general condition, the sequence is arithmetic.