1. The problem asks to identify the pattern of the decay sequence and then find the total decay in the first 5 seconds. 2. The given decay numbers are 24300, 8100, 2700, ... 3. To find the pattern, observe the ratio between consecutive terms: $$\frac{8100}{24300} = \frac{1}{3}, \quad \frac{2700}{8100} = \frac{1}{3}$$ 4. This shows the sequence is a geometric sequence with first term $a = 24300$ and common ratio $r = \frac{1}{3}$. 5. The general term formula for a geometric sequence is: $$a_n = a \times r^{n-1}$$ where $n$ is the term number. 6. So the pattern in words: "Each term is one third of the previous term, starting from 24300." 7. To find the total decay in the first 5 seconds, sum the first 5 terms: $$S_5 = a \frac{1-r^5}{1-r} = 24300 \times \frac{1-(\frac{1}{3})^5}{1-\frac{1}{3}}$$ 8. Calculate the denominator: $$1 - \frac{1}{3} = \frac{2}{3}$$ 9. Calculate the numerator: $$(\frac{1}{3})^5 = \frac{1}{243}$$ So, $$1 - \frac{1}{243} = \frac{242}{243}$$ 10. Substitute back: $$S_5 = 24300 \times \frac{\frac{242}{243}}{\frac{2}{3}} = 24300 \times \frac{242}{243} \times \frac{3}{2}$$ 11. Simplify step-by-step: $$24300 \times \frac{242}{243} = 24300 \times \cancel{\frac{242}{243}}$$ Since $24300 = 243 \times 100$, $$= 100 \times 242 = 24200$$ 12. Now multiply by $\frac{3}{2}$: $$24200 \times \frac{3}{2} = 24200 \times 1.5 = 36300$$ 13. Final answer: The total decay in the first 5 seconds is $36300$.