With the given pattern that continues here, how to write down the nth term of each sequence suggested by the pattern? (A) -2,4,-6,8,-10,.... (B) -1,1,-1,1,-1,.....

1 Answer
Jun 21, 2018

(A) #a_n = (-1)^n * 2n#

(B) #b_n = (-1)^n#

Explanation:

Given:

(A) #-2, 4, -6, 8, -10,...#

(B) #-1, 1, -1, 1, -1,...#

Note that in order to get alternating signs, we can use the behaviour of #(-1)^n#, which forms a geometric sequence with first term #-1#, namely:

#-1, 1, -1, 1, -1,...#

There's our answer to (B) already: The #n#th term is given by #b_n = (-1)^n#.

For (A) note that if we ignore the signs and consider the sequence #2, 4, 6, 8, 10,...# then the general term would be #2n#. Hence we find that the formula we need is:

#a_n = (-1)^n * 2n#