Solve the problem progression and series Concept Map 􀂊Pattern number, progression, and series 􀂊Sigma Notation 􀂊Progression and series arithmetic 􀂊nth term arithmetic progression 􀂊Arithmetic series 􀂊Progression and series geometric 􀂊nth term geometric progression 􀂊Geometric series 􀂊Infinite geometric series Applying the concept of progression and series in the problem-solving Solve the problem progression and series

Pattern number, progression, and series Pattern number is rules in determining the number of one to the next number on each progression is. Progression is organized in a sequential pattern based on the number. Series is the number of all numbers that are on progression. Example : 1. 1, 3, 5, 7, 9, ….  odd number 2. 2, 4, 6, 8, 10, ….  even number 3. 2, 6, 12, 20, 30, ….  rectangular number 4. 1, 3, 6, 10, 15, ….  triangular number 5. 1, 4, 9, 16, 25, ….  square number

Example : Be discovered progression : 2, 5, 10, 17, … Find : a. term to-n formula : U1 = 2 = 1 + 1 = 12 + 1 U2 = 5 = 4 + 1 = 22 + 1 U3 = 10 = 9 + 1 = 32 + 1 U4 = 17 = 16 + 1= 42 + 1 Un = … = … + 1= n2 + 1 so term to-n formula is Un = n2 + 1 b. Numbers on term to-20 (U20) : U20 = 202 + 1 = 401 c. term to which the size of the 170 (Un = 170) Un = 170 = n2 + 1 n2 = 169 n = 13

Sigma Notation is a way to write a short summation. Rule sigma notation Eg ak and bk is term to-k and C constant . 1. If ak = C, then 2. 3. 4. 5.

Example : 1. Indicate series 1 + 4 + 7 + … + 22 with sigma notation : 3.n – 2 = 22  n = 8 2.

Progression and series Arithmetic Arithmetic progression is progression where the difference between the two tribes that sequence is always the same value. Un = a + (n – 1).b where ; Un = The n-th term a = first term b = difference, with b = Un – Un -1 n = order, with n = 1, 2, 3, …

Progression and series Arithmetic Arithmetic series the sum of the members of a finite arithmetic progression. or where ; Sn = series arithmetic Un = The n-th term a = first term b = difference, with b = Un – Un -1 n = order, with n = 1, 2, 3, …

Progression and series Geometric A geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. Un = a.rn-1 where ; Un = The n-th term a = first term r = ratio, with n = order, with n = 1, 2, 3, …

Progression and series Geometric A geometric series is the sum of the numbers in a geometric progression. for r ≠ 1 and r > 1, to be used where ; Sn = series geometric Un = The n-th term a = first term r = ratio, with n = order, with n = 1, 2, 3, …

Progression and series Geometric Infinite series For r ≠ 1 and – 1 < r < 1, to be used infinite series to convergence. where ; S = infinite series a = first term r = ratio, with