1. Refer to the following sequences in R:29(an) := 0, 70, 30, 31, ...35(bn) := 2√6,6√2, 6√6, 18√2, 18√6, 54√/2,...(cn): 8, 1.04, 1.352, 1.7576, 228.488,...(dn): -2.3,-0.2, 1.9, 4, 6.1,...(en): 1, 2, 4, 7, 28, 33,...aDetermine which of the above sequences is(are)* arithmetic (then, give the common difference),* geometric (then, give the common ratio), or* neither (then, give the formula or explain the pattern)

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Answered: 1. Refer to the following sequences in…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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b,, b2, ... be the sequence defined by the explicit formula Let bo D1' b, = c. 6" + D(-5)" for each integer n 2 0, where C and D are real numbers. (a) Find C and D so that b, = 0 and b, = 11. C = D = What is b, in this case? b2 = (b) Find C and D so that b, = 4 and b, = 13. C = D = What is b, in this case? 2.
Use the approach in Gauss's Problem to find the following sums of arithmetic sequences. 293+290+287+284+..+2
1. Refer to the following sequences in R: 29 37 8 (an):= 7' 70' 35' 70' 35 (bn) := 2√6,6√2, 6√6, 18√2, 18√6, 54√2,... (cn): 8, 1.04, 1.352, 1.7576, 228.488,... (dn): -2.3,-0.2, 1.9, 4, 6.1, ... (en): 1, 2, 4, 7, 28, 33, ... Take two arithmetic sequences from the list above and show that as sets, these two are equinumerous. Hint: Assume that the terms of each sequence are the elements of sets X and Y, respectively. Then, define a function f: X->Y and prove that f is bijective.
Answer 8 to 11 answer only 8. What is the next term in the sequence 10,7,3,4,−1 ? A.3 B.5 C.4 D.0 9. What is the general term of the geometric sequence 3,−6,12,−24,.... ? A.an=2(−3)n B.an=3(−2)n C.an=3(−2)n−1 D.an=2(3)n−1 10. What is the general term of the sequence whose first five terms are −1,1/2,−1/4,1/8,−1/16 ? A.an=−(−12)n−1 B.an=−(12)n C.an=−(−12)n D.an=(−12)n−1 11. Find the sum of the first 9999 terms of the sequence 5,5,5,5,5,.... ? A.undefined B.500 C.∞ D.495
1. Find the lowest degree polynomial that generates the sequence {pn} given by 2, 9, 20, 35, 54, 77,.... Here, pi = 2, p2 = 9, p3 = 20, and so on. Make sure you get p7 = 104.
What is the formula for the sequence 0, 1/pi1/2, 4/pi1/3, 9/pi1/4 starting with the term n=1?
Which sequence could described by the explicit definition: tn = 2 · n – 3? {5, 7, 11, 19, 35, ...} {1, 2, 3, 4, 5, 6, ...} {1, -1, -5, -13, ...} O {-1, 1, 3, 5, 7, ..}
Use the Geometric Sum Formula to do the following. (a) Evaluate 1 +3+3² + 3³ + ...+ 310. (b) (Part a, P20, Page 21) Find a formula for 1 + 1 1 1+ x² * (1+x²)² (1+x²)"* 2.

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