Definition
Sequence
Each function whose domain is the counting numbers is called a sequence.
\(f:\mathbb N^+\to\mathbb R\)
\(f(n)=a_n\)
\(a_n\): the nth term, or the general term, of the sequence.
\(n\in\mathbb N^+\).
If \(a_n=k\), where \(k\in\mathbb R\), the sequence is called a constant sequence.
1.
\(a_n=\samefrac{4n-1}{n+2}\)
\(a_7=?\)
2.
\(a_n=\samefrac{6+3n}{n+5}\)
\(a_k=2\)
\(k=?\)
3.
\(a_n=\samefrac{2^n(n+1)!}{n}\)
\(\samefrac{a_{n+1}}{a_n}=?\)
4.
\(a_n=\begin{cases}n-4,&n\text{ odd}\\2n+7,&n\text{ even}\end{cases}\)
\(a_7-a_{10}=?\)
5.
\(a_n=\samefrac{n+4}{k-3n}\)
\(a_6=10\)
\(k=?\)
6.
\(a_{n+5}=\samefrac{3+4a_n}{5}\)
\(a_1=2\)
\(a_{11}=?\)
7.
\(a_n=\samefrac{2n}{n-4}\)
\(b_n=\samefrac8{4-n}\)
\(a_n+b_n=?\)
8.
\(a_{n+2}=\samefrac{3^n}{(n+2)!}\)
\(\samefrac{a_n}{a_{n+1}}=?\)
9.
\(a_{n+1}=\samefrac{10-n}{n+3}a_n\)
\(a_1=2\)
\(a_5=?\)
10.
\(a_n=3n^2-1\)
\(a_7+a_8-2a_5=?\)
11.
\(a_n=(-1)^n(\samefrac34)^n\cdot n!\)
\(\samefrac{a_{n+2}}{a_{n+1}}=?\)