Number Sequences: Problems with Solutions

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