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?

lets look:90 ft will be 9 sections,

100+25+50+75+ 100+ ....25(i)...where i goes from 1 to 8
cost= 100+ Sum25i from i=1 to INT(h-10/10 (h-80)

but this is an arithmetic progression

cost= 100+ n/2(2*25+(n-1)25)
= 100 (4(50+375))=100+425*4=1800

lets look:90 ft will be 9 sections,

100+25+50+75+ 100+ ....25(i)...where i goes from 1 to 8
cost= 100+ Sum25i from i=1 to INT(h-10/10 (h-80)

but this is an arithmetic progression

cost= 100+ n/2(2*25+(n-1)25)
= 100 (4(50+375))=100+425*4=1800

To find out the total cost of building a 90-foot tower, we need to calculate the cost of labor for each section of 10 feet and then add them all together.

Given that the firm charges $100 for labor for the first 10 feet, we can break down the remaining 80 feet into increments of 10 feet, with each increment costing $25 more than the previous one.

Here's a step-by-step breakdown of the cost calculation:

1. Calculate the cost of labor for the first 10 feet: $100

2. Calculate the cost of labor for the next 10 feet: $100 + $25 = $125

3. Calculate the cost of labor for the following 10 feet: $125 + $25 = $150

4. Continue this pattern until we reach the final 10 feet of the 90-foot tower.

- The cost of labor for the third set of 10 feet: $150 + $25 = $175
- The cost of labor for the fourth set of 10 feet: $175 + $25 = $200
- The cost of labor for the fifth set of 10 feet: $200 + $25 = $225
- The cost of labor for the sixth set of 10 feet: $225 + $25 = $250
- The cost of labor for the seventh set of 10 feet: $250 + $25 = $275
- The cost of labor for the eighth set of 10 feet: $275 + $25 = $300
- The cost of labor for the ninth set of 10 feet: $300 + $25 = $325

5. Finally, calculate the cost of labor for the final 10 feet: $325 + $25 = $350

To find the total cost, add up all the individual costs: $100 + $125 + $150 + $175 + $200 + $225 + $250 + $275 + $300 + $325 + $350 = $2475

Therefore, it will cost $2475 to build a 90-foot tower.