(a) Explanation Given that, the high school had 1000 students enrolled at the beginning of 1995. Also, there is a trend that number of students s n beginning a school year was 5% less than that of the previous year and this trend continues over the previous 20 years. Therefore, from the given information, the recurrence relation for n ≥ 1 is obtained as shown below. s n = ( 1 − 5 % ) s n − 1 = ( 1 − 5 100 ) s n − 1 = ( 1 − 0 (b) To determine The formula that expresses s n as a function of n . (c) To determine The number of students in the beginning of the year 2005.

5th Edition

ISBN: 9780134689562

Author: Dossey, John A.

Publisher: Pearson,

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 9.2, Problem 25E

(a)

To determine

The recurrence relation and initial condition representing the given situation.

(b)

To determine

The formula that expresses sn as a function of n.

(c)

To determine

The number of students in the beginning of the year 2005.

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Chapter 9.2, Problem 24E

Chapter 9.2, Problem 26E

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4. Now we'll look at a nonhomogeneous example. The general form for these is y' + p(x)y = f(x). For this problem, we will find solutions of the equation +2xy= xe (a) Identify p(x) and f(x) in the equation above. p(x) = f(x) = (b) The complementary equation is y' + p(x)y = 0. Write the complementary equation. (c) Find a solution for the complementary equation. We'll call this solution y₁. (You only need one particular solution, so you can let k = 0 here.) Y1 = (d) Check that y₁ satisfies the complementary equation, in other words, that y₁+ p(x)y₁ = 0.

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