Math Sequences - Speech or Presentation Example

Arithmetic and Geometric Series January 24, 35: Arithmetic Progression An arithmetic progression refers to a series of numbers where the next number is a sum of the previous number and a fixed element. This means that the difference between all the numbers in an arithmetic sequence is the same. In this question, the series is arithmetic since the difference between preceding terms is 25.In this case, the problem is finding the cost of labor for building 90 feet, where the first 10 feet cost $100, and succeeding feet cost $25 more than preceding feet.

Therefore, the difference between terms, d, is 25, n ­= 9, and a1 is 100. The question requires us to find a9.The formula for an arithmetic sequence is Therefore, Therefore, it is evident that c= 75.To find the 9th term, Therefore, the cost of building 90 feet is $300.37: Geometric sequenceAnalysis of the question indicates that it is a geometric sequence, since the compound interest formula is an example of a geometric sequence. A geometric sequence can be defined as having a constant ratio between terms, with the first term being the base term.

In this case of compound interest, the common ratio between terms is the interest rate, 5%.The formula to use to solve this kind of geometric sequence is;  , where A is the amount after the investment period, P is the original amount invested, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. In this case, Therefore, A = $814.4475.