AMC 8 Daily Practice - The Sum of a Finite Arithmetic Series

Complete problem set with solutions and individual problem pages

Problem 5 Easy

Given the sequence 1, 3, 6, 10, 15, \dots, what is the 20^{\text{th}} term of this sequence?

  • A.

    170

  • B.

    180

  • C.

    190

  • D.

    200

  • E.

    210

Answer:E
Solution

This sequence represents triangular numbers with the n-th term formula: T_n = \sum_{k=1}^n k = \frac{n(n+1)}{2}

For n=20: T_{20} = \frac{20 \times 21}{2} = 210

Final result: \boxed{210}

Related Problems
Problem 3 AMC 8 Daily Practice - The Sum of a Finite Arithmetic Series
Problem 4 AMC 8 Daily Practice - The Sum of a Finite Arithmetic Series
Problem 6 AMC 8 Daily Practice - The Sum of a Finite Arithmetic Series
Problem 7 AMC 8 Daily Practice - The Sum of a Finite Arithmetic Series
Think Academy Powered by ChatGPT