Arithmetic Sequences

A sequence is a set of numbers arranged in a definte order. For example : {1,3,5,7,9...}

A number in a arithmetic sequence can be solved for by using the following equation: a+ (n-1)d

a= the first number in the sequence

n= the number of the term

d= the common difference

Example: What is the fifth term of the sequence when the first number is eight and the common difference is five.

fifth term = 8 + (5-1)5

= 8 + 20

If all the terms in a sequence are added the result is a series.

For instance, if the first five terms of a series are 3, 5, 7, 9 and 11, the sum of the first five terms would be 35.

This is easy to calculate without a formula. What would happen, however, if you were asked to find the sum of the first 100 terms? It would take too long to calculate without a formula.

Therefore, the sum of an arithmetic sequence can be found using the formula:

S= (n/2)[2a + (n-1)d]

Example find the sum of the first 64 terms of a sequence that has a common difference of 3 and the a first number of 4

S = 64/2 [2(4) + (64-1)3]

Simple Interest = principal amount x rate x time period/ 100

If, 200 hundred dollars are initially invested in a bank that makes 4%, what is the interest earned on the account after 3 years.