Recognizing and extending arithmetic sequences

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Presentation transcript:

Recognizing and extending arithmetic sequences Lesson 34 Recognizing and extending arithmetic sequences

sequences A sequence of numbers can be formed using a variety of patterns and operations. A sequence is a list of numbers that follow a rule, and each number in the sequence is called a term of the sequence. An arithmetic sequence has a constant difference between 2 consecutive terms 1,3,5,7,….. Arithmetic sequence 7,4,1,-2,…. Arithmetic sequence 2,6,18,54,… 1,4,9,16

Arithmetic sequence An arithmetic sequence has a constant difference between every 2 consecutive terms To find the common difference, choose any term and subtract it from the previous term. If the sequence does not have a common difference, then it is not arithmetic.

Recognizing arithmetic sequences Determine if the following are arithmetic sequences and find the common difference if they are: 1) 7,12,17,22,… 2) 11,4,-3,-10,… 3) 4,8,16,32,64,… 4) 3,6,12,24,…

Arithmetic sequence formula To find the next term in a sequence: an = a n-1 + d a1 = first term d = common difference n = term number Find the first 4 terms of an arithmetic sequence if the first term is -2 and the common difference is 7 a2 = a 2-1 + 7 a2 = -2 +7 = 5 a3 = a 3-1 + 7 a3 = 5 + 7 = 12

Finding the nth term in arithmetic sequences an = a1 + (n-1)d a1 = 1st term d = common difference Find the 10th term of the sequence 3,11,19,27… 1st term = 3 common difference = 9 a10 = 3 + (10-1)8 = 3 + 9(8)= 3 + 72 = 75

examples Find the 12th term of the sequence 3,10,17,… 3, 3 1/4, 3 1/2, 3 3/4,…. Find the 10th tern of the sequence 1/4, 3/4, 5/4, 7/4, … Use the rule an = -5 + (n-1)(-2) to find the 8th and 20th terms of the sequence