Precalculus by Richard Wright

When you lie down, you will not be afraid; when you lie down, your sleep will be sweet. Proverbs 3:24 NIV

Take this test as you would take a test in class. When you are finished, check your work against the answers. On this assignment round your answers to three decimal places unless otherwise directed.

- Write the first four terms of the sequence \(a_n = n!-n\).
- 256, 192, 144, 108, …
- 20, 14, 8, 2, …
- \(\frac{3}{1}, \frac{4}{4}, \frac{5}{9}, \frac{6}{16}\)
- Simplify \(\frac{3!n!}{4!(n-2)!}\)
- The 3
^{rd}term of an arithmetic sequence is –2 and the 10^{th}term is –16. What is the 5^{th}term? - The 2
^{nd}term of a geometric sequence is 4374 and the 7^{th}term is 576. What is the 5^{th}term? - \(\displaystyle \sum_{k=1}^3 (k-1)^2\)
- \(\displaystyle \sum_{n=1}^{14} 2n^3\)
- \(\displaystyle \sum_{i=1}^{21} -3i + 1\)
- \(\displaystyle \sum_{n=1}^{15} 3(2)^{n-1}\)
- \(\displaystyle \sum_{n=1}^{∞} 5\left(\frac{3}{4}\right)^{n-1}\)
- Use mathematical induction to prove the sum formula \(-4 + -1 + 2 + 5 + \cdots + (3n - 7) = \frac{3}{2}n^2 - \frac{11}{2}n\)
- Use the binomial theorem to expand \(\left(3x + 2\right)^4\).
- Find the coefficient of the term \(x^3\) in \(\left(x + 4\right)^5\).
- Evaluate \(_8C_3\).
- Evaluate \(_8P_3\).
- How many different license plates can be be made if each is 2 letters followed by 2 digits?
- Six people are going to a concert and are sitting in the same row. Fred has a broken leg and has to sit on the aisle and one of his 2 sisters wants to sit next him. How many different sitting arrangements can there be?
- What is the probability that you will randomly guess the answers to 4 out of 4 T/F quiz questions?
- If two coins are flipped, what is the probability of getting 2 tails?
- What is the probability of drawing a face card or a diamond from a standard 52-card deck?

Write the explicit formula for the *n*^{th} term.

Find the sum. Show your work.

- 0, 0, 3, 20
- \(a_n = 256\left(\frac{3}{4}\right)^{n-1}\)
- \(a_n = -6n + 26\)
- \(a_n = \frac{n+2}{n^2}\)
- \(\frac{n(n-1)}{4}\)
- –6
- 1296
- 5
- 22,050
- –672
- 98,301
- 20
- Show work and final step is \(\frac{3k^2 - 5k - 8}{2}\)
- \(81x^4 + 216x^3 + 216x^2 + 96x + 16\)
- 160
- 56
- 336
- 67,600
- 48
- 0.0625
- 0.25
- ≈ 0.423