Geometric Sequences

Notes

Notes for Sequences and Series

 

Practice Problems

\(\textbf{1)}\) Find the next three terms of \(3,6,12, \ldots\)

 

\(\textbf{2)}\) Find the next three terms of \(1,-3,9, \ldots\)

 

\(\textbf{3)}\) Find the next three terms of \(\frac{2}{3},1,\frac{3}{2}, \ldots\) Link to Youtube Video Solving Question Number 3

 

\(\textbf{4)}\) \(a_1=\frac{1}{3},\,r=3,\,\) what is \(a_4\)? Link to Youtube Video Solving Question Number 4

 

\(\textbf{5)}\) \(r=-2,\, a_5=80,\,\) what is \(a_1\)?Link to Youtube Video Solving Question Number 5

 

\(\textbf{6)}\) \(a_1=7,\, a_5=112,\,\) what is \(r\)?

 

Challenge Problems

\(\textbf{7)}\) Find the three geometric means of \(3\) and \(48\) Link to Youtube Video Solving Question Number 7

 

See Related Pages

\(\bullet\text{ Arithmetic Sequences}\)
\(\,\,\,\,\,\,\,a_n=a_1 + d(n-1)\)
\(\bullet\text{ Arithmetic Series}\)
\(\,\,\,\,\,\,\,s_n=\frac{n}{2}(a_1+a_n)…\)
\(\bullet\text{ Geometric Series}\)
\(\,\,\,\,\,\,\,s_n=a_1 \frac{1-r^n}{1-r}…\)
\(\bullet\text{ Infinite Geometric Series}\)
\(\,\,\,\,\,\,\,s_\infty = \frac{a_1}{1-r}\,\,\, |r| \lt 1…\)
\(\bullet\text{ Summation Notation}\)
\(\,\,\,\,\,\,\, \displaystyle \sum_{i=4}^{9} 3i-5 …\)
\(\bullet\text{ Recursive Sequences}\)
\(\,\,\,\,\,\,\, a_{1}=2, \, a_{n+1}=a_{n}+3…\)

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