Question

infinite geometric series quiz

1. a tired frog is jumping across a pond. her first jump will be her longest. she tra...

( ) s = 570 cm
( ) s = 2,700 cm
( ) s = 1,560 cm
( ) s = 3,000 cm

Explanation:

Based on standard curriculum problems matching this exact scenario ("A tired frog is jumping across a pond..."), the full text of the problem is:

"A tired frog is jumping across a pond. Her first jump will be her longest. She travels \( 900\text{ cm} \) on her first jump. Each jump thereafter is \( \frac{2}{3} \) the size of the previous jump. What is the total distance the frog can travel?"

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⚡ Using what you learned: Geometric Series

Step 1: Identify parameters

$$ a_1 = 900 $$

$$ r = \frac{2}{3} $$

Step 2: Apply the sum formula

Since \( |r| < 1 \), the sum of the infinite geometric series is:

$$ S = \frac{a_1}{1 - r} $$

$$ S = \frac{900}{1 - \frac{2}{3}} $$

$$ S = \frac{900}{\frac{1}{3}} $$

$$ S = 900 \times 3 $$

$$ S = 2,700\text{ cm} $$

Answer:

\( S = 2,700\text{ cm} \)