# MATHPOWER TM 10, WESTERN EDITION Chapter 2 Number Patterns 2.5 2.5.1.

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MATHPOWER TM 10, WESTERN EDITION Chapter 2 Number Patterns 2.5 2.5.1

An Arithmetic Sequence is a sequence where each term is formed from the preceding term by adding a constant to the preceding term. Consider the sequence -3, 1, 5, 9. This sequence is found by adding 4 to the previous term. The constant term which is added to each term to produce the sequence is called the Common Difference. 2.5.2 Arithmetic Sequences

-3 + (1)4 -3 + 4 + 4 -3 + (2)4 -3 + 4 + 4 + 4 -3 + (3)4 Continuing with this pattern, the general term is derived as: t n = a + (n - 1) d -3 15 9 a a + da + 2d a + 3d -3 + 4 2.5.3 Arithmetic Sequences

t n = a + (n - 1) d General Term First Term Number or Position of the Term Common Difference 2.5.4 The General Arithmetic Sequence

Given the sequence -5, -1, 3, …: a) Find the common difference. d = t 2 - t 1 = (-1) - ( -5) = 4 Note: The common difference may be found by subtracting any two consecutive terms. b) Find t 10. t n = a + (n - 1) d c) Find the general term. t n = a + (n - 1) d d) Which term is equal to 63? t n = a + (n - 1) d 63 = - 5 + 4n - 4 72 = 4n 18 = n t 18 = 63 a = -5 n = 10 d = 4 t n = ? a = -5 n = ? d = 4 a = -5 n = ? d = 4 t n = 63 t 10 = -5 + (10 - 1) 4 = -5 + (9) 4 t 10 = 31 = -5 + (n - 1) 4 = -5 + 4n - 4 t n = 4n - 9 63 = -5 + (n - 1) 4 2.5.5 Finding the Terms of an Arithmetic Sequence

Find the number of terms in 7, 3, -1, - 5 …, -117. t n = a + (n - 1) d A pile of bricks is arranged in rows. The number of bricks in each row forms a sequence 65, 59, 53, …, 5. Which row contains 11 bricks? How many rows are there? t n = a + (n - 1) d a = 7 n = ? d = -4 t n = - 117 a = 65 n = ? d = - 6 t n = 11 -117 = 7 + (n - 1) (-4) -117 = 7 - 4n + 4 -117 = -4n + 11 -128 = -4n 32 = n 11 = 65 + (n - 1) (-6) -60 = -6n 10 = n a = 65 n = ? d = - 6 t n = 5 5 = 65 + (n - 1) (-6) -66 = -6n n = 11 2.5.6 Finding the Number of Terms of an Arithmetic Sequence The 10th row contains 11 bricks.There are 11 rows in this pile. There are 32 terms in the sequence.

Arithmetic means are the terms that are between two given terms of an arithmetic sequence. Insert five arithmetic means between 6 and 30. 6 _ _ _ _ _ 30 7 terms altogether t n = a + (n - 1)d Therefore, the terms are: a = 6 n = 7 d = ? t n = 30 30 = 6 + (7 - 1)d 30 = 6 + 6d 24 = 6d 4 = d 6,, 30 10,14,18,22, 26 2.5.7 Arithmetic Means

Pages 74 - 76 1 - 43 odd 46, 47, 49, 50 52, 53, 56, 57 2.5.8 Suggested Questions:

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