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

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

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)

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

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 = ………..

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

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

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)