6. During his first week as a salesman, Barney sold 33 products. He challenged himself to sell 3 more products each successive week than he sold the week before. If Barney meets his goal with exactly 3 more products each week, how many products does he sell in week 15 ?

Barney's sales follow a pattern where each week he sells 3 more products than the previous week. Starting with 33 products in week 1, we can determine his sales for week 15 by using the formula for an arithmetic sequence: \( a_n = a_1 + (n - 1) \times d \), where \( a_1 \) is the first term, \( n \) is the week number, and \( d \) is the difference between terms. Plugging in the values, we get \( a_{15} = 33 + (15 - 1) \times 3 = 33 + 42 = 75 \). So in week 15, Barney sells 75 products! If you're curious about sales strategies, this gradual increase in sales can be linked to the concept of setting SMART goals—Specific, Measurable, Achievable, Relevant, Time-bound. By setting a clear target of increasing his sales by a small, manageable amount every week, Barney efficiently builds momentum and confidence in his selling abilities. Keep those goals attainable!