A car company sold 150 cars in a special 6-day sale. Each day, the company sold 6 more than the previous day. How many cars were sold on the 6th day?

### Concept & Formula This problem forms an Arithmetic Progression (A.P.) because sales increase by a constant amount each day. We can use the A.P. sum formula to find the first term, then find the 6th term. $$S_n = \frac{n}{2}[2a + (n - 1)d]$$ $$T_n = a + (n - 1)d$$ ### Step-by-Step Solution * **Given:** * Total sum ($S_n$) = 150 * Number of days ($n$) = 6 * Common difference ($d$) = 6 * **Calculation:** 1. Apply the sum formula to find $a$ (sales on the first day): $150 = \frac{6}{2}[2a + (6 - 1)6]$ 2. Simplify the equation: $150 = 3[2a + 30]$ $50 = 2a + 30$ 3. Solve for $a$: $2a = 20 \Rightarrow a = 10$ 4. Calculate the sales on the 6th day ($T_6$) using the term formula: $T_6 = a + 5d$ $T_6 = 10 + 5(6)$ $T_6 = 10 + 30 = 40$ ### Exam Strategy & Shortcut Use the concept of averages. The average number of cars sold per day is $150 / 6 = 25$. In an arithmetic sequence with an even number of terms, the average falls exactly between the two middle terms (3rd and 4th days). So, the gap between the 3rd and 4th day is 6, meaning the 3rd day is $25 - 3 = 22$, and the 4th day is $25 + 3 = 28$. From the 4th day, add 6 twice to get to the 6th day: $28 + 6 + 6 = 40$. ### Common Pitfall A frequent mistake is solving for $a$ (finding 10) and selecting an option if 10 were present, forgetting that the question specifically asks for the value on the 6th day. Always re-read the final sentence before marking the answer. ### Final Answer **Therefore, the correct answer is 40.**