Week 2- Geometric Series (1.4)

avar2015Math 11

Similarly to the Arithmetic series, we can use a formula to determine variables such as S_n as well as a=t_1 and r. This Formula can be used as demonstrated below to solve for S_7 Where t_5=1024 and r=4.

1. t_n=ar^{n-1}

1024=a(4)^{5-1}

 

\frac{1024}{256}=\frac{(256)}{256}

 

2. S_n=\frac{a(r^n-1)}{r-1}

 

s_7=\frac{4((4^7)-1)}{4-1}

 

s_7=4(16384-1)

 

s_7=\frac{65532}{3}

 

S_7=21844

 

In the first part of this two step equation we determine “a” which is representative of the first term in the series, this is necessary to be able to solve for the 7th term during the second step of the equation. Once we have solved for “a” we substitute the values of all known variables to be able to solve for S_7.

This is how to solve for an unknown variable within a geometric series.

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