For problems #1-4 write out the first six terms of each explicitly defined sequence.
1) \(a_n=\Large\frac{2}{n}\)
2) \(b_n=\Large\frac{n}{n+2}\)
3) \(c_n= 3^n -2n\)
4) \(d_n= \Large\frac{3n+1}{n^3}\)
For problems #5-6 write out the first six terms of each recursively defined sequence.
5) \(a_1=5, a_n=a_{n-1}+3\)
6) \(b_1=-6, b_n= 2 b_{n-1} +n\)
For problems #7-10 write each series in summation notation.
7) \(1, \large\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + ...+ \frac{1}{16}\)
8) \(16 + 2 + (-12) + (-26) + ...\)
9) \(13 + 26 + 39 + ... + 117\)
10) \(3 + \large\frac{3}{8} + \frac{1}{9} + \frac{3}{64} + \frac{3}{125}+ ...\)
For problems #11-13 determine an explicit rule for each given sequence.
11) \(11, 8, 5, 2, -1, ...\)
12) \(2, 5, 10, 17, 26, ...\)
13) \(5, 5, 5, 5, 5, ...\)
For problems #14-18 evaluate the sum.
14) \(\sum\limits_{i=1}^{5} 2i\)
15) \(\sum\limits_{k=1}^{8} 4\)
16) \(\sum\limits_{n=4}^{7} n^3\)
17) \(\sum\limits_{m=1}^{4} \frac{1}{n^2}\)
18) \(\sum\limits_{p=0}^{8} \frac{1}{2^n}\)
19) If you computed the same sum for problem #18 out to 10 terms what happens to your answer? What about out to \(20\) terms? What do these answers seem to be getting closer to?
20) If you did the same process of extending the sum limits for the sum in problem #14 do your answers get closer to some value? If so what is it, if not why?
Review
21) Solve the equation \(\sqrt[3]{25}=(\frac{1}{125})^{4x-1}\)
22) Evaluate \(\ln (e^e)\)
23) What is the x-intercept of \(f(x)=2^{x-3}-4\)?
Solution Bank