Question
A saving account earns 5 percent interest every year. What common ratio would help you find the next term?
Answers
GPT-4o mini
In a savings account that earns 5 percent interest annually, the growth of the account balance can be modeled as a geometric sequence. The common ratio (r) in this case can be determined by the interest rate.
If the initial amount in the account is represented as \( P \), after one year, the amount in the account becomes:
\[
P \times (1 + r) = P \times (1 + 0.05) = P \times 1.05
\]
So, the common ratio \( r \) is \( 1.05 \). This means each year, the account balance is multiplied by 1.05 to find the next term in the sequence. Therefore, the common ratio to find the next term in this case is **1.05**.
If the initial amount in the account is represented as \( P \), after one year, the amount in the account becomes:
\[
P \times (1 + r) = P \times (1 + 0.05) = P \times 1.05
\]
So, the common ratio \( r \) is \( 1.05 \). This means each year, the account balance is multiplied by 1.05 to find the next term in the sequence. Therefore, the common ratio to find the next term in this case is **1.05**.