By Joanne Wachter illustrated by Laura Logan
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Extra info for A Hat to Fit Bun
1, 8, 27, 64, .... ARITHMETIC SERIES An arithmetic series is the addition of successive terms of an arithmetic sequence. , 49 is an arithmetic sequence. So, 21 + 23 + 25 + 27 + ::::: + 49 is an arithmetic series. SUM OF AN ARITHMETIC SERIES Recall that if the first term is u1 and the common difference is d, then the terms are: u1 , u1 + d, u1 + 2d, u1 + 3d, etc. Suppose that un is the last or final term of an arithmetic series. , Sn = (u1 + un) where un = u1 + (n ¡ 1)d 2 so Sn = n (u1 + un ) 2 Sn = or n (2u1 + (n ¡ 1)d) 2 Example 14 Find the sum of 4 + 7 + 10 + 13 + :::: to 50 terms.
B Find the value of u35 for the sequence in a. c Find the sum of the terms of the sequence in a. 2 Insert six numbers between 23 and 9 so that all eight numbers are in arithmetic sequence. 3 Find the formula for un , the general term of: a 86, 83, 80, 77, .... b 34 , 1, 76 , 97 , .... c 100, 90, 81, 72:9, .... CDR Wed Jun 09 17:00:18 2004 0 100 95 75 50 25 5 0 cyan black IB_02 Color profile: Disabled Composite Default screen 56 SEQUENCES AND SERIES (Chapter 2) 4 Write down the expansion of: 5 Write in the form n P 7 P a r2 r=1 (:::::) : r=1 a 4 + 11 + 18 + 25 + :::: for n terms 6 Find the sum of: a 3 + 9 + 15 + 21 + :::: to 23 terms 7 Find the sum of 8 r+3 P r=1 r + 2 b a b 1 4 b 24 + 12 + 6 + 3 + :::: to 12 terms.
CDR Mon Jun 07 14:11:31 2004 0 100 95 75 50 25 5 0 cyan is geometric with black IB_02 Color profile: Disabled Composite Default screen 42 SEQUENCES AND SERIES (Chapter 2) THE ‘GEOMETRIC’ NAME If a, b and c are any consecutive terms of a geometric sequence then c b = fequating common ratiosg a b p p ) b2 = ac and so b = § ac where ac is the geometric mean of a and c. THE GENERAL TERM Suppose the first term of a geometric sequence is u1 and the common ratio is r. u3 = u1 r2 ) Then u2 = u1 r u4 = u1 r3 ) etc.