9.2

A sequence is arithmetic if the differences between consecutive terms are the same. So the sequence...
a1, a2, a3, a4, a5.... an
is arithmetic if there is a number d such that
a2-a1=a3-a2=a4-a3=...=d
The number d is the commin difference of the arithmetic sequence.


ex: 3, 6, 9, 12
d=3

The nth term of an arithmetic sequence has the form
an=dn+c
where d is the common difference between consecutive terms of the sequence and c is a1-d

the sum of a finite arithmetic sequence with n terms is
sn=(n/2)(a1+an)

this formula only works for arithmetic sequences

ex: 1+3+5+7+9+11+13+15+17+19=sn
=n/2(a1+an)
=10/2(1+19)
=100