BACCALAURÉAT GÉNÉRAL ET TECHNOLOGIQUE SESSION 2009 ÉPREUVE SPÉCIFIQUE MENTION « SECTION EUROPÉENNE OU DE LANGUE ORIENTALE »
Académies de Paris-Créteil-Versailles Binôme : Anglais / Mathématiques Sujet7 SEQUENCES
The first part of this page is a summary that can help you to do the exercise.
Arithmetic sequence A sequence {an } is an arithmetic sequence with common difference d if it can be written an = an −1 + d , where n≥2. The nth term of an arithmetic sequence can be written in the form an = a1 + (n − 1)d , where a1 is the first term and d is the common difference. The sum Sn of the first n terms of the sequence with common difference d is n a +a Sn = a1 + a2 + a3 + ... + ak + ... + an = n 1 n or S n = 2a1 + ( n − 1) d . 2 2
EXERCISE In November 2005, the printing firm Farfarelli prints 2100 books. The manager decides to print each month 250 books more than the previous one. Let u1 be the number of thousands of books printed in November 2005 and un be the number of thousands of books printed (n – 1) n months later. 1. Give u2 , u3 , u4 . 2. Give a recursive rule for un . What is the nature of the sequence un ? Give an explicit rule for un . 3. How many books are going to be printed in November 2007? 4. How many books in all have been printed by the Farfarelli firm in 2006? 5. When is the annual production (from January to December) going to be greater than 100,000 books?
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