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5.6.2 The Sum of the First n Terms of
a Geometric Progression
Instructions: Use the following tutorial to help
introduce or reinforce the concept of the Sum of the First n Terms of
a Geometric Progression.
Read through the introduction, then study and familiarize
yourself with the definitions of terms. Next, use
the incremental calculator to study each step of
the process of the Sum of the First n Terms of
a Geometric Progression.
Finally,
use the calculator for examples to quiz yourself.
An geometric progression is a
sequence or pattern of numbers in which each term is
calculated by multiplying r to
the previous number. The sum
Sn of first n terms of a geometric progression is
obtained by using first term a
and the common ratio r
Sn= a[(1 - rn)
/(1 - r)]
for r not equal to 1
Sn= (n)(a)
when r =1
An example of this problem is to find the sum
of the first ten terms of the
sequence 2,4,8,16....
a= 2, n= 10, and r= 2,
Sn=2(1- 210)/(1 - 2)= 2046.
Thus the sum of the first ten terms term 1024.
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