Summation Notation
A child builds a figure with colored blocks
in stages as shown below:
The number of blocks set down in each
stage is a term in the arithmetic sequence
of odd numbers 1, 3, 5 , ….
The final pattern consists of a 6 X 6
square of 36 blocks. So the number of
blocks in the 6th pattern is the sum of the
first six odd numbers:
1 + 3 + 5 + 7 + 9 + 11 = 36
If an is the number of blocks added in the
nth stage and Sn is the total number of
blocks in the nth figure, the total S6 can be
written using summation notation.
6
S6 = a1 + a2+ a3 +…+ a6
a

=
n 1
n
S6 is the value of a series. In general, a
series is an indicated sum of terms of a
sequence.
If the number of terms added is infinite,
the resulting series is an infinite series.
If the # of terms added are finite, the
resulting series is called a finite series.
Find an explicit formula for the blocks
pattern: ____________________
Let’s write the finite arithmetic series from
the pattern of children’s blocks using
summation notation:
6
 (2n  1)
n 1