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AN ARITHMETIC and A GEOMETRY SERIES AN ARITHMETIC and A GEOMETRY SERIES

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1. Finding the Sum of the terms in an Arithmetic sequence

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Remember: Formula of the n- th term of Arithmetic Sequence and Geometry Sequence Formula of the n- th term of Arithmetic Sequence U n =a+(n-1)b where, a = U1 U1 ; b= U 2 - U 1 = U 3 – U2U2 Formula of the n- th term of Geometry Sequence U n =ar n-1 where, a = U1 U1 ; b= U 2 : U 1 = U 3 : U2U2 Formula of the n- th term of Triangular Number Pattern U n =½n(n+1)

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= … = … = … = … … = … … + 2 = … = … = … = … = … … = … … + 2 = …. Calculate the sum of the following series

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Complete the Following Table UnArithmetic Series = Sn U1 U2 U3 U4 U5. U7. U10. Un S 1 = a S 2 = 2a + b S 3 = 3a +3 b S 4 = 4a + 6b S 5 = 5a + 10b. S 7 = ……a + 21b. S 10 =…..a +….. b. S n = ………..

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So, S n = ½ n {2a+(n-1)b } Or S n = ½ n (a+Un) where, a = U1 or term-1 b = U2 - U1 = U3 – U2 or Difference two term

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Banking Problem Mr. Kukuh has a savings account in a bank as much as 650 million rupiahs. Every week he withdraws some money from his savings by using a cheque. With the first cheque, he draws 20 million rupiahs, the second cheque 25 million rupiahs, and so on. The next cheque is 5 million rupiahs more than the previous one. How many weeks can Mr. Kukuh draw all his savings, if there is no administration fee? On Page 180 of student book

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CONCLUSION If the terms in an ascending arithmetic sequence are totaled, they will form an ascending arithmetic series. Similarly, if the terms in a descending arithmetic sequence are totaled, they will form a descending arithmetic series. Formula of arithmetic series Sn = ½ n {2a+(n-1)b } Or Sn = ½ n (a+Un)

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