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Sagot :
Answer:
91
Step-by-step explanation:
To find the total number of mucus people eliminated by the medicine, let's first observe the pattern in the number of mucus people entering the lungs each day:
- Day 1: 1 mucus person
- Day 2: 4 mucus people
- Day 3: 9 mucus people
- Day 4: 16 mucus people
Notice that each day, the number of new mucus people is a perfect square:
- Day 1: 1² = 1 mucus person
- Day 2: 2² = 4 mucus people
- Day 3: 3² = 9 mucus people
- Day 4: 4² = 16 mucus people
Therefore, the pattern rule for the number of new mucus people entering the lungs (aₙ) on the nth day is:
[tex]a_n = n^2[/tex]
The sigma notation that represents the sum of the number of mucus people entering the lungs each day from day 1 to day 6 is:
[tex]\displaystyle \sum_{n=1}^{6} n^2[/tex]
Expanding this notation, we get:
[tex]\displaystyle \sum_{n=1}^{6} n^2=1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2[/tex]
Calculate the sum:
[tex]\displaystyle \sum_{n=1}^{6} n^2= 1 + 4 + 9 + 16 + 25 + 36 \\\\\\ \sum_{n=1}^{6} n^2 = 91[/tex]
So, the medicine eliminates a total of 91 mucus people from the teacher's lungs.
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