Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004 AND Mathematical Studies Standard Level Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman Oxford University Press, 2012 Applying Arithmetic Sequences and Series Susan wants to buy a flat. She has to pay for the flat in 20 year installments. The first installment is 5500 €. Each installment is 500 € more than the one before. A. Write down the value of the second and third installment. B. Calculate the value of the final installment. C. Show that the total amount Susan would pay for the flat is 205000 €. u1 = 5500 and d = 500 u2 = 6000 € and u3 = 6500 € u20 = u1 + (n – 1)d = 5500 + (20 – 1)500 = 15,000 € n S n 2u1 (n 1)d 2 S20 = 𝟐𝟎 𝟐 (2(5500) + (20 – 1)500) S20 = 205,000 € The sales of Smartphones are growing every year. At the end of 2006, the number sold was 25,000,000. At the end of 2010, the number sold was 35,800,000. Assuming that the sales follow an arithmetic sequence, calculate: A. the number pf Smartphones sold at the end of 2008 B. the predicted number of Smartphones sold at the end of 2015 u1 = 25,000,000 AND u5 = u1 + 4d = 35,800,000 35,800,000 = 25,000,000 + 4d d = 2,700,000 2008 would be u3 u3 = u1 + 2d = 25,000,000 + 2(2,700,000) = 30,400,00 2015 would be u10 u10 = u1 + 9d = 25,000,000 + 9(2,700,000) = 49,300,00 Applying Geometric Sequences and Series Penelope is starting her first job. She will earn $24,000 in the first year and her salary will increase by 4% every year. Calculate how much Penelope will earn in her fourth year of work. u1 = $24,000 AND r = 1.04 un u1r n 1 u4 = 2400 x 1.043 u4 = $26996.74 A ball is vertically dropped. It reaches a height of 1.6 m on the first bounce. The height of each subsequent bounce is 80% of the previous bounce. A. Find the height the ball reaches on the 6th bounce. B. Find the sum of the first seven terms of this sequence. u1 = 1.6 m un u1r n 1 Sn = u1 (r n – 1) (r – 1) AND r = 0.80 u6 = 1.6 x 0.85 S7 = 1.6 (0.8 7 – 1) (0.8 – 1) u6 = 0.524 m S7 = 6.32 m