Question

a delivery is offering a special promotion for frequent customers. on the first delivery of the month, they apply a discount of $4 to the delivery. for each subsequent delivery, the discount increases by $3. so the second delivery costs $7, the third delivery costs $10, and so on. a customer plans to use the service for a total of 13 deliveries in one month. the company wants to calculate the total money saved with discounts the customer will benefit from over the 13 deliveries. show your work here.

Explanation:

Step1: Identify the arithmetic - sequence

The discounts form an arithmetic sequence with first term $a_1 = 4$ and common difference $d = 3$. The number of terms $n = 13$.

Step2: Use the sum formula for an arithmetic sequence

The sum formula of an arithmetic - sequence is $S_n=\frac{n(a_1 + a_n)}{2}$, where $a_n=a_1+(n - 1)d$. First, find $a_{13}$:
$a_{13}=a_1+(13 - 1)d=4+(12)\times3=4 + 36=40$.

Step3: Calculate the sum of the sequence

Then, use the sum formula $S_{13}=\frac{13\times(4 + 40)}{2}=\frac{13\times44}{2}=13\times22 = 286$.

Answer:

286