2. Theorem:
The sum of the integers from 1 to n
is given by the formula:
( )1
2
1
+= nnSn
3.
4. Arithmetic Sequence
It is a sequence in which the
difference between consecutive
terms is constant and has the form:
Note: An arithmetic sequence
exhibit constant growth
( )dnadadaa 1,,2,, 1111 −+++
7. Arithmetic Series
A series is an indicated sum of
terms of a sequence. If the terms
form an arithmetic sequence with
first term a1 and common
difference d, the indicated sum of
terms is called an arithmetic
series. The sum of the first n
terms, represented as Sn, is
10. Arithmetic Series
Let Sn = a1 + a2 + … + an be
an arithmetic series with
constant difference d, then:
( )[ ]
2
12 1 dnan
Sn
−+
=
11.
12. Geometric Sequence
(Or Geometric Progression) is a
sequence in which each term
after the first is obtained by
multiplying the preceding term
by a common multiplier. The
common multiplier is called the
common ratio of the sequence.
14. Geometric Series
A geometric series is the indicated
sum of a geometric sequence. The
following are examples of
geometric series:
1 + 2 + 4 + 8 + …
8 + 4 + 2 + 1 + …
1 + (-4) + 16 + (-64) + …
15. Geometric Series
The sum of the first n terms of a
geometric sequence that has a first
term a1 and a common ration r is
given by:
( ) .1anyfor,
1
11
≠
−
−
= r
r
ra
S
n
n
