To model the situation with a recursive sequence, we need to define the health points of Meera's character in relation to the damage taken from enemies.
Let's denote:
- \( H(n) \): the health points after \( n \) hits.
- \( D(n) \): the total damage taken after \( n \) hits.
Initially, Meera's character has 122 health points, which gives us the base case for our sequence:
- Base case: \[ H(0) = 122 \]
After the first hit, Meera's health will decrease based on the damage from that hit. Let’s denote the damage taken from the \( n \)-th hit as \( d_n \). Then, we can express the health after the \( n \)-th hit recursively as:
- Recursive formula: \[ H(n) = H(n-1) - d_n \]
Where \( d_n \) is the damage taken during the nth hit.
To define \( D(n) \), which is the total damage taken before being hit for the \( n \)-th time, we can set it up as follows:
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Base case: \[ D(0) = 0 \]
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Recursive formula: \[ D(n) = D(n-1) + d_n \]
In summary:
- The health points of Meera's character after \( n \) hits can be modeled by: \[ H(n) = H(n-1) - d_n \quad \text{for } n \geq 1 \]
- The total damage taken before being hit for the \( n \)-th time is: \[ D(n) = D(n-1) + d_n \quad \text{for } n \geq 1 \]
This recursive model accurately captures the mechanics of damage taken and remaining health points through successive enemy hits.
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