What is the formula for the sequence #2, -1, 4, -7, 10, -13, 16,...# ?
1 Answer
Aug 20, 2017
The given sequence is matched by the formula:
#a_n = (-1)^n (-2+3(n-1))#
or if you prefer:
#a_n = (-1)^n (3n-5)#
Explanation:
No infinite sequence is determined purely by a finite number of terms, unless you are given further information - e.g. that the sequence is arithmetic or geometric.
That having been said, note that if we multiply the terms of the given sequence by
#-2, 1, 4, 7, 10, 13, 16,...#
which is (as far as it goes) an arithmetic sequence with initial term
So a formula that fits the original sequence can be written:
#a_n = (-1)^n (-2+3(n-1))#