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Dr. Raja Latif. Finite Mathematics.Pg:1
Dr. Raja Latif. 5.3 ANNUITIES
Objective
:
To introduce the notions of ordinary
annuities and annuities due. To use geometric series to
model the present value and future value of an annuity.
Geometric Sequence: If
a
and
r
are nonzero real
numbers, the infinite list of numbers
a
,
ar
,
ar
2
,
ar
3
,
ar
4
,...
is called a geometric
sequence. The number
a
is called the first term of the
sequence,
ar
is the second term,
ar
2
is the third term,
and so on. Thus for any
n
1,
ar
n
1
is the
nth
term of
the sequence. Each term in the sequence is
r
times the
preceding term. The number
r
is called the common ratio
of the sequence.
The sum
S
n
of the first
n
terms of the geometric
sequence is called the geometric series:
S
n
a
ar
ar
2
ar
3
ar
4
...
ar
n
1
.
If
r
1,
then
S
n
a
a
a
a
...
a
na
.
If
r
1,
multiply both sides of the equation by
r
to get
rS
n
ar
ar
2
1
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View Full DocumentDr. Raja Latif. Finite Mathematics.Pg:2
ar
3
ar
4
...
ar
n
.
Now subtract corresponding sides of equation
from
equation
.
rS
n
ar
ar
2
ar
3
ar
4
...
ar
n
S
n
ar
ar
2
ar
3
ar
4
...
ar
n
1
rS
n
S
n
a
ar
n
S
n
r
1
a
r
n
1
S
n
a
r
n
1
r
1
.
Sum of Geometric Series: The
sum s
of a geometric
series of
n
terms whose first term is
a
and common ratio
is
r
is given by
S
n
a
r
n
1
1
r
,
r
1.
ExampleLGR217. Find the sum of the first six terms of
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 Spring '09
 Dr.RajaLatif
 Math, Geometric Series

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