Calculate the Day: Solving for When Daniel's Savings Reach Exactly $29

To determine if Daniel can save exactly $29, we model his savings as an arithmetic sequence.</p> <ul> <li><strong>Step 1: Identify the given information</strong></li> </ul> <p>Initially, Daniel puts in$15, and he adds $2 daily. We are looking for the day when the total savings equals$29.

• Step 2: Set up the sequence formula

The $n$-th term of an arithmetic sequence is given by:

$a_n = a_1 + (n-1) \cdot d$

Where:

• $a_1 = 15$, the amount on the first day
• $d = 2$, the daily addition
• $a_n = 29$, the amount we want to achieve

• Step 3: Solve for $n$

Set up the equation:

$29 = 15 + (n-1) \cdot 2$

Simplifying:

$29 = 15 + 2n - 2$

$29 = 13 + 2n$

$16 = 2n$

$n = 8$

Therefore, Daniel will have exactly $29 on the eighth day.</p> <p><strong>Conclusion:</strong></p> <p>Yes, it is possible for Daniel to save exactly$29, and it will occur on the eighth day.