What is the sum of all the odd integers between 6 and 60?
Answer (1)
SOLUTION:Step 1: List the given values.Since we are talking about odd integers, the first and the last term must be 7 and 59, which are close to 6 and 60, respectively.Consecutive odd integers always have a difference of 2.[tex]\begin{aligned} & a_1 = 7 \\ & a_n = 59 \\ & d = 2 \end{aligned}[/tex]Step 2: Find the number of terms.[tex]\begin{aligned} n & = \frac{a_n - a_1}{2} + 1 \\ & = \frac{59 - 7}{2} + 1 \\ & = \frac{52}{2} + 1\\ & = 26 + 1 \\ & = 27 \end{aligned}[/tex]Step 3: Solve for the sum of the terms of an arithmetic sequence.[tex]\begin{aligned} S & = \frac{n}{2}(a_1 + a_n) \\ & = \frac{27}{2}(7 + 59) \\ & = (13.5)(66) \\ & = \boxed{891} \end{aligned}[/tex]Hence, the sum of all the odd integers between 6 and 60 is 891.
