Elementary Grade 4 Math Word Problems. Arithmetic Sequence.
Calculate the expression: the sum from 5 to 200 with common difference 5, minus the sum from 4 to 199 with common difference 5.
Let's solve this step by step. First, we group the terms by pairing each term from the first sequence with the corresponding term from the second sequence. This gives us 5 minus 4, plus 10 minus 9, plus 15 minus 14, and so on. Each pair equals 1, and there are 40 such pairs, so the answer is 40.
Let's visualize this solution. Each pair of corresponding terms from the two sequences has a difference of exactly 1. We have 5 minus 4 equals 1, 10 minus 9 equals 1, 15 minus 14 equals 1, and so on, up to 200 minus 199 equals 1. Since there are 40 such pairs, the final answer is 40.
Therefore, the final answer to this arithmetic sequence problem is 40. This demonstrates how we can simplify complex calculations by recognizing patterns and grouping terms strategically.