List the first four terms of the sequence whose nth term is a_n = (-1)^n + 1 / n. Solve the recurrence relation a_n = 2a_n-1 + 8a_n-2 with initial conditions a_0 = 1, a_1 = 4. can be used as a prefix though for certain compounds. a_1 = 15, d = 4, Write the first five terms of the sequence and find the limit of the sequence (if it exists). For the sequences shown: i) Find the next 2 numbers in the sequence ii) Write the rule to explain the link between consecutive terms in the form [{MathJax fullWidth='false' a_{n+1}=f(a_n) }] iii) Find a formula for the general term and of the sequence, assuming that the pattern of the first few terms continues. These kinds of questions will be some of the easiest on the test so take some time and drill the katakana until you have it mastered. Calculate the first 10 terms (starting with n=1) of the sequence a_1=-2, \ a_2=2, and for n \geq 3, \ a_n=a_{n-1}-2a_{n-2}. 1, 3, \frac{9}{2}, \frac{9}{2}, \frac{27}{8}, \frac{81}{40}, (A) \frac{77}{80} \\(B) \frac{79}{80} \\(C) \frac{81}{80} \\(D) \frac{83}{80} \\(E) \frac{87} Find a formula for the nth term of the sequence in terms of n. 1, 0, 1, 0, 1, \dots, Compute the sum: \sum_{i \in S} \left(i^2 + 1\right) where S = \{1, 3, 5, 7\}. Consider a fish population that increases by 8\% each month and from which 300 fish are harvested each month. (Hint: Begin by finding the sequence formed using the areas of each square. . (Assume n begins with 1.) What is a recursive rule for -6, 12, -24, 48, -96, ? if lim n { n 5 + 2 n n 2 } = , then { n 5 + 2 n n 2 } diverges to infinity. Suppose you gave your friend a total of $630 over the course of seven days. Raise 5 5 to the power of 2 2. Then so is \(n^5-n\), as it is divisible by \(n^2+1\). If the limit does not exist, explain why. Question. .? 4.1By mathematical induction, show that {a n } is increasing and bounded above by 3 . If it converges, find the limit. If arithmetic, give d; if geometric, give r; if Fibonacci's give the first two For the given sequence 5,15,25, a. Classify the sequences as arithmetic, geometric, Fibonacci, or none of these. If it converges, find the limit. Direct link to Jerry Nilsson's post 3 + 2( 1) a_n = 2^{n-1}, Write the first five terms of the sequence. \begin{cases} b(1) = -54 \\b(n) = b(n - 1) \cdot \frac{4}{3}\end{cases}. 1.5, 2.5, 3.5, 4.5, (Hint: You are starting with x = 1.). a_n = n(2^(1/n) - 1), Determine if the series will converges or diverges or neither if the series converges then find the limit: a_n = cos ^2n/2^n, Determine if the series will converges or diverges or neither if the series converges then find the limit: a_n = (-1)^n/2 square root{n} = lim_{n to infinty} a_n=, Determine whether the following sequence converges or diverges.
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