For problems #1-5 write out the first six terms of the recursively defined sequence
1) \(a_1=4, a_n=a_{n-1}+7\)
2) \(a_1= 64, a_n=\frac{1}{2} a_{n-1}\)
3) \(a_1=5, a_n=n +a_{n-1}\)
4) \(a_1=3, a_{n-1}= -2n^2\)
5) \(a_1=1, a_2=1, a_n=a_{n-1}+a_{n-2}\)
For problems #6-10 decide if the sequence is arithmetic or geometric and then write a recursively defined rule for the sequence
6) \(3, 12, 48, 192, ...\)
7) \(4, -8, 16, -32, ...\)
8) \( 73, 64, 55, 46, ...\)
9) \(1, r, r^2, r^3,...\)
10) \(0, d, 2d, 3d, ...\)
Review
11) If there are \(42\) grams of substance \(\beta\) in a sample at time zero, and \(8\) grams of the substance in the sample after \(12\) hours, what is the half life of substance \(\beta\)?
12) Which is a better investment for the next \(10\) years? By how much?
Option A: \(\$1000\) compounded semiannually at \(3\%\) annual interest.
Option B: \(\$1000\) compounded continuously at \(2.9\%\) annual interest.
13) Let \(f(x)=e^{5x}\). Solve for \(x\), \(e^{35}=f(x)\).
14) What is(are) the extraneous solution(s) to the following equation, \(\log_{3} x + \log_{3} (x-6) = 3\)?
15) Evaluate \(\log_{25} 125\) without using technology.
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