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Answer :
Kylie starts with \(\$145\) in her piggy bank, and each month she adds \(\$20\). This means that at the end of the first month, the amount in her piggy bank is the initial amount:
$$
a_1 = 145.
$$
For each subsequent month, she adds \(\$20\) to the amount from the previous month. Therefore, for \( n \geq 2 \), the recursive formula for the amount \( a_n \) is:
$$
a_n = a_{n-1} + 20.
$$
This rule tells us that to find the amount at the end of any month, we add \(\$20\) to the amount from the previous month. In summary, the recursive function that models the total amount in Kylie's piggy bank is:
$$
a_n = a_{n-1} + 20 \quad \text{with} \quad a_1 = 145.
$$
Thus, the correct answer is the option:
$$
a_n = 20 + a_{n-1} \quad \text{and} \quad a_1 = 145.
$$
$$
a_1 = 145.
$$
For each subsequent month, she adds \(\$20\) to the amount from the previous month. Therefore, for \( n \geq 2 \), the recursive formula for the amount \( a_n \) is:
$$
a_n = a_{n-1} + 20.
$$
This rule tells us that to find the amount at the end of any month, we add \(\$20\) to the amount from the previous month. In summary, the recursive function that models the total amount in Kylie's piggy bank is:
$$
a_n = a_{n-1} + 20 \quad \text{with} \quad a_1 = 145.
$$
Thus, the correct answer is the option:
$$
a_n = 20 + a_{n-1} \quad \text{and} \quad a_1 = 145.
$$
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