# 90-foot tower - Problem Solving

by Latonya Smith
(Texas)

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?

### Comments for 90-foot tower - Problem Solving

 Mar 05, 2012 90-foot tower by: Staff Question: by Latonya Smith (Texas) 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? Answer: each 10 feet represents a term in an arithmetic sequence The 90 foot tower has 9 terms To sum all the terms, the formula for an arithmetic series can be used: S_n = (1/2) * n (a_1 + a_n ) The total cost of the tower is the average of the first and last terms times the number of terms (in this case, 9 terms) a_n = a with a subscript of n (this is the nth term in the series) a_1 = a with a subscript of 1 (this is the 1st term in the series) n = number of terms d = difference between consecutive terms (the common difference) The first term in the series is known a_1 = 100 The last term in the series can be computed using the following formula: a_n = a_1 + (n - 1) * (d) Applying the notation to your problem a_1 = 100 d (the common difference) = 25 The 9th term (representing the last 10 feet of construction): n = 9 a_n = a_1 + (n - 1) * (d) a_9 = 100 + (9 - 1) * (25) a_9 = 100 + (8) * (25) a_9 = 100 + 200 a_9 = 300 The total cost of the tower is: S_n = (1/2) * n (a_1 + a_n ) S_9 = (1/2) * 9 (100 + 300 ) S_9 = (1/2) * 9 * (400) S_9 = 1800 >>> the final answer is: \$1,800 Thanks for writing. Staff www.solving-math-problems.com