2016 as a product **a*b** where **a** is the # of members and** b** the average of those members : 1*2016, 2*1008, 3*672...21*96...

96*21 ...1008*2, 2016*1.

To each of those pairs corresponds an arithmetic sequence uniquely defined by a,b,d (d=2) :

e.g. 3*672**=>**670,672,674; 21*96=>76,78,80, ..., 96, ...114,116.

There are 36 pairs of a*b, if listed by increasing** a** we get first

eighteen consisting of positive numbers only, and for every sequence **S(i****)** defined by **a(i***)*,b(i) there exists a corresponding

sequence **S(j***)* such that **j=37-i** and **a(i***)=*b(j) & a(j*)=*b(i):

S(2) with a*b=2*1008 corresponds to S(35) generated by 1008*2 .

However the first two sequences hardly fit the definition of **arithmetic progression** ( sequence of numbers such that the difference of any two successive members of the sequence is a constant):

2016 - there are no successive members,

1007,1009 - no **constant **difference.

The total number of arithmetic sequences - S(3) to S(36) - is **34**.

*Edited on ***January 24, 2015, 2:56 am**