Posts Tagged ‘sequences’

Week 2-Geometric sequences

This week we learned about geometric sequences and series. A Geometric sequence differs from an arithmetic sequence because instead of adding a common difference, a common ratio is multiplied by the term to get the next term.

the equation used to find a term in a sequence is

 

t_n=ar^{n-1}

in this equation t_1 is represented by a

for example: 5,10,20,40… find t_{10}

 

t_{10}=5(2)^{10-1}

 

t_{10}=5(2)^9

 

t_{10}=5(512)

 

t_{10}=2560

 

A finite geometric series can be found using the equation

Week 1 – My Arthmetic Sequence

 

4, 9, 14, 19, 24

d=5, t_1=4

 

t_n=t_1+(n-1)d

 

t_n=4+(n-1)5

 

t_n=4+5n-5

 

t_n=5n-1

using this information, we can find any value of t using the equation t_n=5n-1. We can plug in any term into n to find t_n

 

this equation will work for any term within the sequence, as long as the starting term and common difference are constant. If either of these change it is no longer an arithmetic sequence.

To find S_{50}, the sum of all 50 terms, we must use the equation S_n={n}{2}(a+1)

In this equation, n= number of terms(50) and a= the first term(4)

 

S_{50}={50}{2}(4+1)

 

S_{50}=25(5)

 

S_{50}=125