13.sequences-and-series of pre calculuss

pre calculus

1. SEQUENCES and series

2. A sequence is a function whose domain is the set of positive integers or the set {1, 2, 3, … n}. It is a list of numbers separated by commas. The sequence with nth term is usually denoted by { }.   A series represents the sum of the terms of a sequence. It is a sum of numbers (separated by “+” or “-” sign. The sequence with nth term is usually denoted by { }, and the associated series is given by S = + + + . . . .  

3. Determine the first five terms of each defined sequence, and give their associated series. {2 – n} {1 + 2n + 3 } {(-1)} {1 + 2 + 3 + . . . + n}  

4. Fibonacci sequence The sequence { } defined by = + for n ≥ 3, where = = 1, is called a Fibonacci sequence. Its terms are 1, 1, 2, 3, 5, 8, 13, . . .  

5. arithmetic sequence An arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant (called the common difference) to the preceding term.

6. geometric sequence A geometric sequence is a sequence in which each term after the first is obtained by multiplying the preceding term by a constant (called the common ratio).

7. harmonic sequence If { } is an arithmetic sequence, then the sequence with n th term = is a harmonic sequence.  

8. WRITE SEQ IF THE GIVEN ITEM IS A SEQUENCE, AND WRITE SER IF IT IS A SERIES.

9. WRITE A IF THE SEQUENCE IS ARITHMETIC, F IF IT IS GEOMETRIC, F IF FIBONACCI, AND O IF IT IS NOT ONE OF THE MENTIONED TYPES.