Math Problem Statement
Performance Task 13 Donation for a Cause
- You are running a foundation for street children. Mr. Felipe Cortejos, a rich benefactor, offers two options for his donations: Option A: To give Php 1 000 on day 1, Php 999 on day 2, Php 998 on day 3, with the process to end after 1 000 days. Option B: To give Php 1 on day 1, Php 2 on day 2, Php 4 on day 3, for 1 000 days. You have to tell him today which option you want to take. Which of the two options results in more money for the foundation? Show your computations.
Solution
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequence
Geometric Sequence
Formulas
Sum of an arithmetic sequence: S_n = n/2 * (2a_1 + (n-1) * d)
Sum of a geometric sequence: S_n = a_1 * (r^n - 1) / (r - 1)
Theorems
Arithmetic series summation
Geometric series summation
Suitable Grade Level
Grades 10-12
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