AMC 8 Daily Practice Round 6

Complete problem set with solutions and individual problem pages

Problem 5 Easy

What is the value of 4 - 6 + 8 - 10 + \dots + 2020 - 2022 + 2024?

  • A.

    1014

  • B.

    1010

  • C.

    -1010

  • D.

    1016

  • E.

    1018

Answer:A

Through observation, we find that the sum of every two consecutive numbers is -2.

Grouping the sequence into pairs, we calculate the total number of terms as: 2024 \div 2 - 1 = 1011 numbers, 1011 \div 2 = 505\dots1 which forms 505 complete groups with 1 remaining term.

The original expression can thus be rewritten as: 4 - 6 + 8 - 10 + \dots + 2020 - 2022 + 2024 = (4 - 6) + (8 - 10) + \dots + (2020 - 2022) + 2024 = \underbrace{(-2) + (-2) + \dots + (-2)}_{505 \text{ terms}} + 2024 = (-2) \times 505 + 2024 = -1010 + 2024 = 1014.

The final result is \boxed{1014}.

Related Problems
Problem 3 AMC 8 Daily Practice Round 6
Problem 4 AMC 8 Daily Practice Round 6
Problem 6 AMC 8 Daily Practice Round 6
Problem 7 AMC 8 Daily Practice Round 6
Think Academy Powered by ChatGPT