find the sum of all odd numbers from 1 to 50 in solving please
Answer (1)
SOLUTION:Step 1: List the given values.Since we are talking about odd integers, the first and the last term must be 1 and 49, which are close to 1 and 50, respectively.Consecutive odd integers always have a difference of 2.[tex]\begin{aligned} & a_1 = 1 \\ & a_n = 49 \\ & d = 2 \end{aligned}[/tex]Step 2: Find the number of terms.[tex]\begin{aligned} n & = \frac{a_n - a_1}{2} + 1 \\ & = \frac{49 - 1}{2} + 1 \\ & = \frac{48}{2} + 1\\ & = 24 + 1 \\ & = 25 \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{25}{2}(1 + 49) \\ & = (12.5)(50) \\ & = \boxed{625} \end{aligned}[/tex]Hence, the sum of all the odd numbers from 1 to 50 is 625.
