Chapter VI Sequence and series of number and its use in solving problem

( A. Definition of pattern of number) (1. Pattern of number) 1. Sequence of odd integer sequence 1, 3, 5, 7, Sequence of even integer sequence 2, 4, 6, 8,.... ( B. Pattern of number on pascal triangle ) The pictures shows a sequence: 1 = = = = 10 Therefore, sequence 1, 3, 6, 10,... Is sequence of numbers in pascal triangle. Pascal triangle can be used to determine coefficient much term (x + y) n with n is original number. 1. Sequence of odd integer sequence 1, 3, 5, 7, Sequence of even integer sequence 2, 4, 6, 8,....

(2. Sequence and series of number) Numbers that are sorted with certain pattern(rule) forms a sequence number. For example, sequence of a. 40, 44, 48, 52, 56,..., 116 b. 1, 3, 5, 7, 9,..., 51 and c. 2, 4, 6, 8, 10,...,98. A. Sequence of number Sum of terms on the sequence called series. Hence, If U 1, U 2, U 3,..., Un are a sequence number therefore U 1 + U 2 + U U n called series. B. Series number

A sequence U 1, U 2, U 3,..., U n, U n + 1 are called arithmetic sequence if for each n is original number that fit with U n + 1 – U n = U n – U n–1 =... = U 2 – U 1 = b. C. A rithmetic sequence Arithmetic series noted by summing terms on arithmetic sequence. To declare total of n the first term on arithmetic sequence uses symbol S n. D. Arithmetic series Generally, geometric sequence defined as following. A sequence U1, U2, U3,..., Un, Un+1 called geometric sequence if for each n is original number E. Geometric sequence

Total n of first term on geometric series is. F. Geometric series

Example in solving problem: In a regency, civil population on 1 st January 2008 is people. If level of growth of population in the regency is 10% for every year, calculate total of civil in the regency on 1 st January Solving: Step 1 Write what is known what is the being questioned. Step 2 Make mathematic model of the problem. Step 3 Determine the total civil on 1 st January 2018.