A small business owner is tracking her monthly sales of a new product. She realizes her sales form an arithmetic sequence. She sold 50 units in the first month, and every other month she sold 15 units more than the previous month. Another product's sales follow a geometric sequence where its first month is 30 units and doubles each month.  How many units of the first product were sold in the 6th month? A. 120 units B. 125 units C. 130 units D. 140 units

The sales of the first product follow an arithmetic sequence, where the first term \(a_1 = 50\) and the common difference \(d = 15\). To find the number of units sold in the 6th month, we use the formula for the \(n\)-th term of an arithmetic sequence:

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

For the 6th month (\(n = 6\)):

\[
a_6 = 50 + (6 - 1) \cdot 15
\]
\[
a_6 = 50 + 5 \cdot 15
\]
\[
a_6 = 50 + 75 = 125
\]

Thus, the number of units sold in the 6th month is **125 units**, which corresponds to option **B**.

Would you like more details or explanations on any step?

Here are some related questions to consider:

1. What would be the total sales of the first product after 6 months?
2. How do you calculate the sum of an arithmetic sequence over a period of time?
3. What are the sales in the 10th month for the first product?
4. How do the sales compare for the second product in the 6th month?
5. How do geometric sequences grow compared to arithmetic sequences?

**Tip**: Arithmetic sequences grow by a constant amount, while geometric sequences grow by a constant factor.

A small business owner is tracking her monthly sales of a new product. She realizes her sales form an arithmetic sequence. She sold 50 units in the first month, and every other month she sold 15 units more than the previous month. Another product's sales follow a geometric sequence where its first month is 30 units and doubles each month. How many units of the first product were sold in the 6th month? A. 120 units B. 125 units C. 130 units D. 140 units

Learn how to calculate the 6th-month sales of a product using an arithmetic sequence where the first month's sales are 50 units and increase by 15 units each month. This problem involves algebraic concepts suitable for Grades 8-10.

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