Problem 41 - College Algebra

Question

Find the sum of the first 60 positive even integers.

Step-by-Step Solution

Answer

The sum of the first 60 positive even integers is 3660.

Step 1: Identify the first, last, and number of terms

An even number is any number that can be expressed as 2n, where n is an integer. Therefore, in this case, the first term (a_1) is 2*1 = 2 and the last term (a_n) is 2*60 = 120. The number of terms (n) is 60.

Step 2: Use the formula for the sum of an arithmetic series

The formula for the sum S of an arithmetic series is given by \(S_n = n/2 * (a_1 + a_n)\), where \(a_1\) is the first term, \(a_n\) is the last term, and n is the number of terms. Substituting the values from Step 1 into this formula gives \(S_{60} = 60/2 * (2 + 120)\).

Step 3: Compute the sum

Calculate the expression from Step 2 to get the sum of the first 60 positive even integers. So, \(S_{60} = 30 * (122) = 3660\).