The document discusses the formula for calculating the sum of an arithmetic series. It provides the general formula as Sn = (a + l)n/2 if the last term (l) is known, and as Sn = (2a + (n-1)d)/2 otherwise. It also gives examples of using the formula to calculate specific sums.

1. Sum Of An Arithmetic
Series

2. Sum Of An Arithmetic
Series
S n  a  a  d  a  2d    l  2d  l  d  l

3. Sum Of An Arithmetic
Series
S n  a  a  d  a  2d    l  2d  l  d  l
S n  l  l  d  l  2d    a  2 d  a  d  a

4. Sum Of An Arithmetic
Series
S n  a  a  d  a  2d    l  2d  l  d  l
S n  l  l  d  l  2d    a  2 d  a  d  a
2S n  a  l  a  l  a  l    a  l  a  l  a  l

5. Sum Of An Arithmetic
Series
S n  a  a  d  a  2d    l  2d  l  d  l
S n  l  l  d  l  2d    a  2 d  a  d  a
2S n  a  l  a  l  a  l    a  l  a  l  a  l
 na  l 

6. Sum Of An Arithmetic
Series
S n  a  a  d  a  2d    l  2d  l  d  l
S n  l  l  d  l  2d    a  2 d  a  d  a
2S n  a  l  a  l  a  l    a  l  a  l  a  l
 na  l 
n
S n  a  l  if we know l
2

7. Sum Of An Arithmetic
Series
S n  a  a  d  a  2d    l  2d  l  d  l
S n  l  l  d  l  2d    a  2 d  a  d  a
2S n  a  l  a  l  a  l    a  l  a  l  a  l
 na  l 
n
S n  a  l  if we know l
2
otherwise;

8. Sum Of An Arithmetic
Series
S n  a  a  d  a  2d    l  2d  l  d  l
S n  l  l  d  l  2d    a  2 d  a  d  a
2S n  a  l  a  l  a  l    a  l  a  l  a  l
 na  l 
n
S n  a  l  if we know l
2
otherwise;
n
S n  a  a  n  1d 
2

9. Sum Of An Arithmetic
Series
S n  a  a  d  a  2d    l  2d  l  d  l
S n  l  l  d  l  2d    a  2 d  a  d  a
2S n  a  l  a  l  a  l    a  l  a  l  a  l
 na  l 
n
S n  a  l  if we know l
2
otherwise;
n
S n  a  a  n  1d 
2
n
S n  2a  n  1d 
2

10. e.g. i  If a  3 and T6  96, find S6

11. e.g. i  If a  3 and T6  96, find S6
n
S n  a  l 
2

12. e.g. i  If a  3 and T6  96, find S6
n
S n  a  l 
2
6
S6  3  96
2

13. e.g. i  If a  3 and T6  96, find S6
n
S n  a  l 
2
6
S6  3  96
2
 297

14. e.g. i  If a  3 and T6  96, find S6
n
S n  a  l 
2
6
S6  3  96
2
 297
ii  Find the sum of the first 100 even numbers

15. e.g. i  If a  3 and T6  96, find S6
n
S n  a  l 
2
6
S6  3  96
2
 297
ii  Find the sum of the first 100 even numbers
a  2, d  2 and n  100

16. e.g. i  If a  3 and T6  96, find S6
n
S n  a  l 
2
6
S6  3  96
2
 297
ii  Find the sum of the first 100 even numbers
a  2, d  2 and n  100
n
S n  2a  n  1d 
2

17. e.g. i  If a  3 and T6  96, find S6
n
S n  a  l 
2
6
S6  3  96
2
 297
ii  Find the sum of the first 100 even numbers
a  2, d  2 and n  100
n
S n  2a  n  1d 
2
100
S100  4  992
2

18. e.g. i  If a  3 and T6  96, find S6
n
S n  a  l 
2
6
S6  3  96
2
 297
ii  Find the sum of the first 100 even numbers
a  2, d  2 and n  100
n
S n  2a  n  1d 
2
100
S100  4  992
2
 50  202
 10100

19. iii  The sum of the first 10 numbers is 100 and the first 5 numbers is 25.
Find a, d and the general term.

20. iii  The sum of the first 10 numbers is 100 and the first 5 numbers is 25.
Find a, d and the general term.
S10  100

21. iii  The sum of the first 10 numbers is 100 and the first 5 numbers is 25.
Find a, d and the general term.
S10  100
10
2a  9d   100
2

22. iii  The sum of the first 10 numbers is 100 and the first 5 numbers is 25.
Find a, d and the general term.
S10  100
10
2a  9d   100
2
2a  9d  20

23. iii  The sum of the first 10 numbers is 100 and the first 5 numbers is 25.
Find a, d and the general term.
S10  100 S5  25
10
2a  9d   100
2
2a  9d  20

24. iii  The sum of the first 10 numbers is 100 and the first 5 numbers is 25.
Find a, d and the general term.
S10  100 S5  25
10 5
2a  9d   100 2a  4d   25
2 2
2a  9d  20

25. iii  The sum of the first 10 numbers is 100 and the first 5 numbers is 25.
Find a, d and the general term.
S10  100 S5  25
10 5
2a  9d   100 2a  4d   25
2 2
2a  9d  20 a  2d  5

26. iii  The sum of the first 10 numbers is 100 and the first 5 numbers is 25.
Find a, d and the general term.
S10  100 S5  25
10 5
2a  9d   100 2a  4d   25
2 2
2a  9d  20 a  2d  5
2a  9d  20
2a  4d  10

27. iii  The sum of the first 10 numbers is 100 and the first 5 numbers is 25.
Find a, d and the general term.
S10  100 S5  25
10 5
2a  9d   100 2a  4d   25
2 2
2a  9d  20 a  2d  5
2a  9d  20
2a  4d  10
5d  10

28. iii  The sum of the first 10 numbers is 100 and the first 5 numbers is 25.
Find a, d and the general term.
S10  100 S5  25
10 5
2a  9d   100 2a  4d   25
2 2
2a  9d  20 a  2d  5
2a  9d  20
2a  4d  10
5d  10
d  2 a  1

29. iii  The sum of the first 10 numbers is 100 and the first 5 numbers is 25.
Find a, d and the general term.
S10  100 S5  25
10 5
2a  9d   100 2a  4d   25
2 2
2a  9d  20 a  2d  5
2a  9d  20
2a  4d  10
5d  10
d  2 a  1
Tn  a  n  1d

30. iii  The sum of the first 10 numbers is 100 and the first 5 numbers is 25.
Find a, d and the general term.
S10  100 S5  25
10 5
2a  9d   100 2a  4d   25
2 2
2a  9d  20 a  2d  5
2a  9d  20
2a  4d  10
5d  10
d  2 a  1
Tn  a  n  1d
 1  n  12
 2n  1

31. iii  The sum of the first 10 numbers is 100 and the first 5 numbers is 25.
Find a, d and the general term.
S10  100 S5  25
10 5
2a  9d   100 2a  4d   25
2 2
2a  9d  20 a  2d  5
2a  9d  20
2a  4d  10
5d  10
d  2 a  1
Tn  a  n  1d
 1  n  12
 2n  1  a  1, d  2, Tn  2n  1

32. 10
iv   3n  6
n1

33. 10
iv   3n  6
n1
a  3, l  24, n  10

34. 10
iv   3n  6
n1
a  3, l  24, n  10
n
S n  a  l 
2

35. 10
iv   3n  6
n1
a  3, l  24, n  10
n
S n  a  l 
2
10
S10   3  24
2
 105

36. 10
iv   3n  6
n1
a  3, l  24, n  10
n
S n  a  l 
2
10
S10   3  24
2
 105
Exercise 6I; 2ace, 4bd, 5ac, 7c, 8f, 9, 11ac, 13be, 16a
17bc, 19, 20a*