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Notes
Arithmetic Recursive Series
\(a_n=a_{n-1}+d\)
Arithmetic Recursive Series
\(a_n=a_{n-1}+d\)
Geometric Recursive Series
\(a_n=r \cdot a_{n-1}\)
Geometric Recursive Series
\(a_n=r \cdot a_{n-1}\)
Practice Problems
\(\textbf{1)}\) Find the first 5 terms of this sequence \(a_{1}=2, \, a_{n+1}=a_{n}+3\)
\(\textbf{2)}\) Find the first 3 terms of this sequence \(a_{1}=-3, \, a_{n+1}=a_{n}+2n\)
\(\textbf{3)}\) Find the first 3 terms of this sequence \(a_{1}=0, a_{n+1}=5a_{n}-8\)
\(\textbf{4)}\) Find the first 5 terms of this sequence \(a_{1}=5,a_{2}=3 a_{n+2}=a_{n+1}-2a_{n}\)
\(\textbf{5)}\) Write an explicit rule for the sequence \(a_{1}=3, \, a_{n}=4a_{n-1}\)
Related Pages
\(\text{Arithmetic Sequences}\Rightarrow\)
\(\,\,\,\,\,\,\,a_n=a_1 + d(n-1)\)
\(\text{Geometric Sequences}\Rightarrow\)
\(\,\,\,\,\,\,\,a_n=a_1 \cdot r^{(n-1)}\)
\(\text{Arithmetic Series}\Rightarrow\)
\(\,\,\,\,\,\,\,s_n=\frac{n}{2}(a_1+a_n)\)
\(\text{Geometric Series}\Rightarrow\)
\(\,\,\,\,\,\,\,s_n=a_1 \frac{1-r^n}{1-r}\)
\(\text{Infinite Geometric Series}\Rightarrow\)
\(\,\,\,\,\,\,\,s_\infty = \frac{a_1}{1-r}\,\,\, |r| \lt 1\)
\(\text{Summation Notation}\Rightarrow\)
\(\,\,\,\,\,\,\, \displaystyle \sum_{i=4}^{9} 3i-5 \)
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