Arithmetic Sequences In this section, you will learn how to identify arithmetic sequences, calculate the nth term in arithmetic sequences, find the number.

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Presentation transcript:

Arithmetic Sequences In this section, you will learn how to identify arithmetic sequences, calculate the nth term in arithmetic sequences, find the number of terms in an arithmetic sequence and find the sum of arithmetic sequences.

Identifying an Arithmetic Sequence Sequences of numbers that follow a pattern of adding a fixed number from one term to the next are called arithmetic sequences. The following sequences are arithmetic sequences: Sequence A: 5 , 8 , 11 , 14 , 17 , ... Sequence B: 26 , 31 , 36 , 41 , 46 , ... Sequence C: 20 , 18 , 16 , 14 , 12 , ...

Common Difference Because these sequences behave according to this simple rule of adding a constant number to one term to get to another, they are called arithmetic sequences. So that we can examine these sequences to greater depth, we must know that the fixed numbers that bind each sequence together are called the common differences. Sometimes mathematicians use the letter d when referring to these types of sequences.

Sequences Mathematicians also refer to generic sequences using the letter a along with subscripts that correspond to the term numbers as follows: Generic Sequence: a1, a2, a3, a4, ... This means that if we refer to the fifth term of a certain sequence, we will label it a5. a17 is the 17th term. This notation is necessary for calculating nth terms, or an, of sequences. d can be calculated by subtracting any two consecutive terms in an arithmetic sequence. d = an - an - 1, where n is any positive integer greater than 1.

Calculating the nth term In general, the nth term of an arithmetic progression, with first term a and common difference d, is: a + (n - 1)d . Find the 8th term of the sequence 9,12,15…. a=9, d=3, n=8 30

Questions An arithmetic sequence has 10 as its first term and a common difference of -4. Find its 12th term (цn= a+(n-1)d) -34 The 15th term of an arithmetic sequence is 45. If the first term is -11, find the common difference 4

To Do Exercise 12.1.1, page 342 (Q 1- 7)