Study of Geometric and Arithmetic Sequence - Essay Example

For example 1, 4, 7, 10 and so on. In a geometric sequence, each successive term is obtained by multiplying (or dividing) the previous term by a constant. For example 2, 6, 18, 54 and so on. A person hired a firm to build a CB radio tower. The firm charges $100 for labour for the first 10 feet. After that, the cost of the labour 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.

The labour cost for the construction of the tower is $100 for the first 10 feet. After that, each new invoice is $25 more than the previous one. Hence the invoice numbers look like this: 100, 125, 150, 175 and so on. There is a constant difference of 25 between two successive terms which tells us this is an arithmetic sequence.
In other words, each year the existing balance is multiplied by 1.05. Hence 1.05 is the common ratio and every term of the sequence is found by multiplying the previous term with this common ratio. This means we have a geometric sequence at hand.

Exercise 37 had a constant ratio of 1.05 between successive balances each year in the savings account. Hence we used the geometric sequence formula to calculate our final balance. We can use arithmetic sequences to calculate the average performance of a data set of like say the average marks of a class as the data is distributed evenly around the median. Geometric sequences can be used to capture the growth of the data set like the growth in the returns of a mutual fund, equity, etc.