The document discusses methods for calculating the sum of terms in an arithmetic series. It provides the general formula for the sum as Sn = (a + l)n/2 where a is the first term, l is the last term, n is the number of terms, and d is the common difference. It also shows how to calculate the sum given specific values of a, d, and n. Examples are worked through demonstrating how to use the formulas.

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  2d  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  2d  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  2d  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  2d  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  2d  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  2d  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  2d  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 S 6

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

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

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

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