Created by Mr. Lafferty Maths Dept. Arithmetic Series Find nth term of Arithmetic Series Sum of Arithmetic Series www.mathsrevision.com nth and sum of Geometric Series 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Arithmetic Series Learning Intention Success Criteria 1. We are learning how Pascal’s triangle can help us expand polynomials. 1. Be able to construct Pascal’s triangles. www.mathsrevision.com 2. Be able to expand polynomials brackets using Pascal’s triangle. 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Arithmetic Series An Arithmetic Series is a sequence which differs by the same amount each time Let the first term be a and the difference be d then 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Arithmetic Series Example : Find a formula for the nth term of the sequence 9, 12, 15,... and the 20th term. a = 9 d = 12 - 9 = 3 u20 = 3(20) + 6 un = a + (n – 1)d u20 = 60 + 6 un = 9 + 3(n – 1) u20 = 66 un = 3n + 6 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Arithmetic Series The sum of an Arithmetic Series Rewriting the terms in reverse Now adding each corresponding terms 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Arithmetic Series For a infinite number of terms then a = first term l = last term 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Arithmetic Series Example : For 2 + 5 + 8 + 11 + ... Find u15 and S8. a = 2 d = 3 un = 2 + 3(n – 1) un = 3n – 1 S8 = 100 u15 = 3(15) - 1 = 44 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Arithmetic Series Example : If the first term is 37 and difference is -4. Find u15 and S8. un = a + (n – 1)d u15 = 37 - 4(15 – 1) u15 = -19 S8 = 184 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Arithmetic Series Example : Find the number of terms in the series 5 + 8 + 11 ... + 62. a = 5 d = 3 un = a + (n – 1)d 5 + 3(n – 1) = 62 3n + 2 = 62 n = 20 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Arithmetic Series Example : Find the sum of 2 + 4 + 6 + 8 .... + 146 a = 2 d = 2 un = a + (n – 1)d 2 + 2(n – 1) = 146 2n = 146 S8 = 5402 n = 73 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Arithmetic Series Example : The second term of an Arith. sequence is 18 and fifth is 21. Find the common difference, first term and sum of the first 10 terms un = a + (n – 1)d (u2) a + d = 18 (u5) a + 4d = 21 d = 1 S10 = 215 a = 17 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Arithmetic Series Exercise 1 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Geometric Series A Geometric sequence is one in which the ratio of each term to the previous is a constant called the common ratio (r) 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Sum of Geometric Series Let Sn denote the sum of n terms, a the first term and r the common ratio. If r > 1 better to use r ≠ 1 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Sum of Geometric Series Find u10 for the Geometric Sequence :- 144, 108, 81, 60¾ 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Sum of Geometric Series Find S19 for the Geometric Sequence :- 3, -6, 12, -24 ... 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Sum of Geometric Series A Geometric Series has the first term 27 and common ratio Take logs Find the least number of terms the series can have if its sum exceeds 550. 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Sum of Geometric Series A Geometric Series has the first term 27 and common ratio Take logs Find the least number of terms the series can have if its sum exceeds 550. 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Sum of Geometric Series Given find Sub into 14-Sep-18 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Arithmetic Series Exercise 2A 14-Sep-18 Created by Mr. Lafferty Maths Dept.