PreCalculus – Introduction to Sequences Name______
You learned about sequences in Algebra One. Read over these paragraphs to review the basic concepts, then do the problems.
A sequence is a function whose domain is the set of Natural numbers {1, 2, 3, 4, 5, …}. The numbers in the sequence are referred to as the terms of the sequence. The sequence 2,4,6,8,10,….. would look like the ordered pairs (1, 2) (2,4) (3,6) (4,8) and (5, 10). Instead of using function notation, sequences are usually written using subscripted notation. The terms are written as where the subscript refers to the number of the term.
The first 4 terms of the sequence are which simplify to .
ARITHMETIC SEQUENCE If a sequence of values follows a pattern of adding a fixed amount from one term to the next, it is referred to as an arithmetic sequence. The number added to each term is constant (always the same). The fixed amount is called the common difference, d, referring to the fact that the difference between two successive terms yields the constant value that was added. To find the common difference, subtract the first term from the second term.
GEOMETRIC SEQUENCE If a sequence of values follows a pattern of multiplying a fixed amount (not zero) times each term to arrive at the following term, it is referred to as a geometric sequence. The number multiplied each time is constant (always the same). The fixed amount multiplied is called the common ratio, r, referring to the fact that the ratio (fraction) of the second term to the first term yields this common multiple. To find the common ratio, divide the second term by the first term.
For each sequence, tell whether it is arithmetic, geometric or neither. Also state the common difference or common ratio.
Use the given formula to generate the first 5 terms of the sequence. Then identify it as arithmetic, geometric or neither. Tell the common difference or common ratio.