Can you please explain step by step on how to do each of these two problems below? And then tell me whether it involves an arithmetic sequence or a geometric sequence I also need the work shown out for both problems thank you.

1). A person hired a firm to build a CB radio tower. The firm charges $100 for labor for the first 10 feet. After that, the cost of the labor for each succeeding 10 feet is $25 more than the preceding 10 feet. That is, the next 10 feet will cost $125, the next 10 feet will cost $150, etc. How much will it cost to build a 90-foot tower?

2). A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly. At the end of 10 years, how much money will be in the savings account?

ost = 100 + 125 + 150 + 175 + for 9 terms

This is an arithmetic series
a = 100
d = 25
n = 9
Sum(9) = (9/2)(2(100) + (9-1)(25))
= (9/2)(200 + 200) = 1800

2)

amount = 500(1.05)^10 = 814.45

what is the arithmetic oe 3,5,7,9,and 11

Mary has been working at the university for 25 years, with an excellent record of service. As a result, the board wants to reward her with a bonus to her retirement package. They are offering her $75,000 a year for 20 years, starting one year from her retirement date and each year for 19 years after that date. Mary would prefer a one-time payment the day after she retires. What would this amount be if the appropriate interest rate is 7%?

1) To solve this problem, let's break it down step by step:

Step 1: Determine the cost of labor for each 10-foot increment.
- The cost of labor for the first 10 feet is $100.
- For each succeeding 10 feet, the cost increases by $25.
- So, the cost of the second 10 feet is $100 + $25 = $125.
- The cost of the third 10 feet is $125 + $25 = $150.
- This pattern continues for each 10-foot increment.

Step 2: Calculate the total cost for the 90-foot tower.
- Since the cost increases by $25 for each 10-foot increment, we can calculate the cost for each increment and sum them up.
- 90 feet can be divided into 9 increments of 10 feet each.
- The cost for the first 10 feet is $100.
- The cost for the second 10 feet is $100 + $25 = $125.
- The cost for the third 10 feet is $125 + $25 = $150.
- Continuing this pattern, the cost for the ninth 10 feet is $100 + $25 * 8 = $300.
- So, the total cost would be $100 + $125 + $150 + $175 + $200 + $225 + $250 + $275 + $300 = $1,600.

Answer: It will cost $1,600 to build a 90-foot tower.

Regarding the sequence type, this problem does not involve an arithmetic or a geometric sequence because the cost is not increasing in a consistent manner.

2) To solve this problem, follow these steps:

Step 1: Calculate the interest earned each year.
- The amount deposited is $500.
- The annual interest rate is 5%.
- The interest is compounded yearly, so it is added to the initial amount at the end of each year.
- The formula for calculating compound interest is: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
- In this case, P = $500, r = 5% (or 0.05), n = 1 (compounded yearly), and t = 10 years.
- Plugging in these values into the formula, we get A = 500(1 + 0.05/1)^(1*10).

Step 2: Calculate the final amount.
- Evaluate the expression we obtained in step 1.
- A = 500(1 + 0.05)^10.
- Using a calculator or algebraic software, this evaluates to approximately $814.44.

Answer: At the end of 10 years, there will be approximately $814.44 in the savings account.

Regarding the sequence type, this problem does not involve an arithmetic or a geometric sequence. It involves compound interest calculation.