# Number Sequences: Problems with Solutions

Problem 1
The sequence $$\{a_n\}$$ is defined as $$a_1=137$$ and $$a_{n+1}-a_n=0$$ for $$n \ge 1$$. Find $$a_{8999}$$
Problem 2
Find $$a_{15}$$ if $$a_1=4$$, $$a_2=6$$ and $$a_{n+2}+a_n=2a_{n+1}$$.
Problem 3
If $$a_n=\frac{4n-1}{n}$$, find $$a_{19}$$
Problem 4
$$x_n=\frac{2n+8}{4+3n}$$. Calculate $$x_2$$.
Problem 5
$$a_n=-3+2^n+5^{n-3}$$. Find $$a_5$$
Problem 6
Let the sequence $$\{a_n\}$$ be defined as $$a_n=2^n+n$$. Is it increasing or decreasing?

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