Grades 9-10 Video Solutions 2026-2026_9-10

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Question 7. What is the value of the expression 1 minus 2, minus 3 minus 4, minus 5 minus 6, and so on, until minus 25 minus 2026? Is it A, negative 1013, B negative 1011, C 1011, D 1013, or E 2024? First, let's count the number of terms we have. In our expression, we include every number from 1 to 2026. And we include two numbers in each term, in each pair of parentheses. So the total number of terms is 2026 divided by 2, or 1013. Now let's look at the value of each of these terms. 1 minus 2 is negative 1. 3 minus 4 is negative 1. 5 minus 6 is negative 1. For each of our terms, we are taking an integer and subtracting the next consecutive integer. And so, all of these terms are equal to negative 1. Now, let's evaluate the expression. 1 minus 2 is negative 1. For each of the 1012 terms after that, we are subtracting a negative 1. And so we have minus 1, minus 1012 times negative 1, or minus 1 plus 1012, which gives us 1011, or C.

Keywords

arithmetic sequence

subtraction

pairing terms

negative one

expression evaluation