# 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))#