AMC 10 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 22 Medium

 

Given that \{a_n\} and \{b_n\} are arithmetic sequences,

a_1 = 1, \quad b_1 = 2, \quad a_3 + b_3 = 5.

What is the value of a_{2023} + b_{2023}?

  • A.

    2027

  • B.

    2026

  • C.

    2025

  • D.

    2024

  • E.

    2023

Answer:C

Because \left\{ {{a}_{n}} \right\} and \left\{ {{b}_{n}} \right\} are arithmetic sequences, then \left\{ {{a}_{n}}+{{b}_{n}} \right\} is an arithmetic sequences.

a_{1}+b_{1}=3, {{a}_{3}}+{{b}_{3}}=5. Thus, the common difference of \left\{ {{a}_{n}}+{{b}_{n}} \right\} is 1,

{{a}_{2023}}+{{b}_{2023}}={{a}_{3}}+{{b}_{3}}+2020\times 1=2025,

Choose \boxed{\text{B}}.

Related Problems
Problem 20 AMC 10 Daily Practice Round 1
Problem 21 AMC 10 Daily Practice Round 1
Problem 23 AMC 10 Daily Practice Round 1
Problem 24 AMC 10 Daily Practice Round 1
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