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

2. 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.
2. Be able to expand polynomials brackets using Pascal’s triangle.
14-Sep-18
Created by Mr. Lafferty Maths Dept.

3. 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.

4. 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 = = 3
u20 = 3(20) + 6
un = a + (n – 1)d
u20 =
un = 9 + 3(n – 1)
u20 = 66
un = 3n + 6
14-Sep-18
Created by Mr. Lafferty Maths Dept.

5. 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.

6. 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.

7. Created by Mr. Lafferty Maths Dept.
Arithmetic Series
Example :
For 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.

8. 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 = (15 – 1)
u15 = -19
S8 = 184
14-Sep-18
Created by Mr. Lafferty Maths Dept.

9. Created by Mr. Lafferty Maths Dept.
Arithmetic Series
Example :
Find the number of terms in the series
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.

10. Created by Mr. Lafferty Maths Dept.
Arithmetic Series
Example :
Find the sum of
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.

11. 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.

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

13. 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.

14. 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.

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

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

17. 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.

18. 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.

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

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