AN and
ARITHMETIC 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
Un=a+(n-1)b where, a = U1 ; b= U2 - U1 = U3 – U2 Formula of the n-th term of Geometry Sequence
Un=arn-1 where, a = U1 ; b= U2 : U1 = U3 : U2
Formula
of
the
n-th
term
of
Triangular
Un=½n(n+1)
Number
Pattern
Calculate the sum of the following series 1. 2. 3. 4. 5. 6.
5 + 8 + 11 + 14 + 17 = ….. 93 + 88 + 83 + 78 + 73 + 68 = …. 3 + 6 + 12 + 24 + 48 = …. 64 + 32 + 16 + 8 + 4 = …. 6 + 10 + 14 + 18 + … + 170 = …. 205 + 198 + 191 + 184 + … + 2 = ….
Complete the Following Table Un
Arithmetic Series = Sn
U1
S1 = a
U2
S2 = 2a + b
U3 U4 U5 . . U7 . . U10 . . Un
S3 = 3a +3 b S4 = 4a + 6b S5 = 5a + 10b . . S7 = ……a + 21b . . S10 =…..a +….. b . . Sn = ………..
So, Sn = ½ n {2a+(n-1)b } Or Sn = ½ n (a+Un) where, a = U1 or term-1 b = U2 - U1 = U3 – U2 or Difference two term
On Page 180
of student book
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?
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)