Write Your Own Story Book by Louie Stowell

By Louie Stowell

Aspiring younger writers will love this enjoyable task e-book filled with tricks, guidance and convenient projects for writing breath-taking tales. the 1st 1/2 the ebook is stuffed with writing advice, recommendations and strategies to make each tale a masterpiece, with worthwhile actions on arising with principles, writing from varied issues of view and developing characters, settings and tale traces. the second one 1/2 the booklet is filled with tale topics to put in writing approximately, from homicide mysteries to stories from outer house. With plenty of covered house to fill, every one job comes with feedback for characters, settings and items to write down into the tale in addition to inquiries to recommended the mind's eye.

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A Show that the sequence is arithmetic. b Find the formula for the general term un . c Find the 100th term of the sequence. d Is i 828 ii 2341 a member of the sequence? 9¡2 = 7 16 ¡ 9 = 7 23 ¡ 16 = 7 30 ¡ 23 = 7 a So, assuming that the pattern continues, consecutive terms differ by 7. ) the sequence is arithmetic with u1 = 2, d = 7. , un = 7n ¡ 5 ii Let un = 2341 ) 7n ¡ 5 = 2341 ) 7n = 2346 ) n = 335 17 Let un = 828 7n ¡ 5 = 828 ) 7n = 833 ) n = 119 ) 828 is a term of the sequence. In fact it is the 119th term.

CDR Wednesday, 24 October 2007 12:47:21 PM PETERDELL IB_HL-2ed 58 SEQUENCES AND SERIES (Chapter 2) Example 4 Find the general term un for an arithmetic sequence with u3 = 8 and u8 = ¡17: ) ) u3 = 8 u8 = ¡17 u1 + 2d = 8 u1 + 7d = ¡17 fun = u1 + (n ¡ 1)dg :::: (1) :::: (2) We now solve (1) and (2) simultaneously: ¡u1 ¡ 2d = ¡8 u1 + 7d = ¡17 ) 5d = ¡25 ) d = ¡5 fadding the equationsg u1 + 2(¡5) = 8 ) u1 ¡ 10 = 8 ) u1 = 18 So in (1) Now ) ) ) un un un un Check: u3 = 23 ¡ 5(3) = 23 ¡ 15 =8 X = u1 + (n ¡ 1)d = 18 ¡ 5(n ¡ 1) = 18 ¡ 5n + 5 = 23 ¡ 5n u8 = 23 ¡ 5(8) = 23 ¡ 40 = ¡17 X Example 5 Insert four numbers between 3 and 12 so that all six numbers are in arithmetic sequence.

B Find un and hence find the 15th term. 0 2 5 95 100 50 75 25 0 5 1 For the geometric sequence with first two terms given, find b and c: a 2, 6, b, c, .... b 10, 5, b, c, ..... c 12, ¡6, b, c, ..... CDR Monday, 22 October 2007 4:02:54 PM PETERDELL IB_HL-2ed 62 SEQUENCES AND SERIES (Chapter 2) 4 Show that the sequence 8, ¡6, 4:5, ¡3:375, .... is geometric and hence find the 10th term as a decimal. p p 5 Show that the sequence 8, 4 2, 4, 2 2, .... is geometric. Hence find, in simplest form, the general term un .

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