solve using arithmetic sequence3. Situation: Suppose you decide to save $50 every month. If you start with $50 in the first month, your savings will grow by $50 each month.givenFirst month: $50Second month: $50 + $50 = $100Third month: $100 + $50 = $150, and so on.solution?2. Situation: A classroom has desks arranged in rows, with each row having two more desks than the previous row. The first row has 5 desks.givenRow 1: 5 desksRow 2: 5+2 = 7 desksRow 3: 7 + 2 = 9 desks, and so on.solution?3. Situation: A person starts with a salary of $40,000 per year and gets a raise of $2,000 each year.givenYear 1: $40,000Year 2: $40,000 + $2,000 = $42,000Year 3: $42,000 + $2,000 = $44,000, and so on.solution?
Answer (1)
1. SOLUTION:[tex]\begin{aligned} a_n & = a_1 + (n - 1)d \\ & = 50 + (n - 1)(50) \\ & = 50 + 50n - 50 \\ a_n & = \boxed{50n} \end{aligned}[/tex]2. SOLUTION:[tex]\begin{aligned} a_n & = a_1 + (n - 1)d \\ & = 5 + (n - 1)(2) \\ & = 5 + 2n - 2 \\ a_n & = \boxed{2n + 3} \end{aligned}[/tex]3. SOLUTION:[tex]\begin{aligned} a_n & = a_1 + (n - 1)d \\ & = 40,000 + (n - 1)(2,000) \\ & = 40,000 + 2,000n - 2,000 \\ a_n & = \boxed{2,000n + 38,000} \end{aligned}[/tex]
