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Chapter 11: Problem 41

Find the sum of the first 60 positive even integers.

Short Answer

Expert verified
The sum of the first 60 positive even integers is 3600.

Step by step solution

01

Identify the series and it's properties

The first 60 positive even integers form an arithmetic series, where the first term \(a_1 = 2\) (the first positive even integer) and the common difference \(d = 2\). The task is to find the sum of the first 60 terms of this series.
02

Find the value of the last term

As it is an arithmetic sequence, the nth term \(a_n\) of the sequence can be found using the formula \(a_n = a_1 + (n - 1) * d\). Here, \(n = 60\) hence, \(a_{60} = 2 + (60 - 1) * 2 = 120\).
03

Apply the sum formula and solve

Now that we have values for \(a_1\), \(a_n\), and \(n\), we can substitute these into the sum formula. The sum \(S\) of the first 60 positive even integers is given by \(S = \frac{n}{2}(a_1 + a_n) = \frac{60}{2}(2 + 120) = 30 * 122 =3600\).

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. There's no end to the number of geometric sequences that I can generate whose first term is 5 if I pick nonzero numbers \(r\) and multiply 5 by each value of \(r\) repeatedly.

Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises \(71-76\). A pendulum swings through an arc of 16 inches. On each successive swing, the length of the arc is \(96 \%\) of the previous length. $$ \begin{array}{cccc} {16,} & {0.96(16),} & {(0.96)^{2}(16),} & {(0.96)^{3}(16)} \\ {\text { Ist }} & {2 \text { nd }} & {3 \text { rd }} & {4 \text { th }} \\ {\text { swing }} & {\text { swing }} & {\text { swing }} & {\text { swing }} \end{array} $$ After 10 swings, what is the total length of the distance the pendulum has swung?

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Use this information to solve Exercises \(47-48 .\) The mathematics department of a college has 8 male professors, 11 female professors, 14 male teaching assistants, and 7 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a professor or a male.
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