The document shows how to find the general term of a sequence by setting up a table with the terms, taking the differences between terms, and setting up equations to solve for coefficients a and b in the general term formula an + b. It works through examples of finding the general terms for sequences such as 5, 12, 19, 26, 33, etc. and provides a quiz to find the general terms for additional sequences.

2. EXAMPLE:
FIND THE GENERAL TERM OF
THE SEQUENCE
5, 12, 19, 26, 33, . . .

3. PREPARE A TABLE
n 1 2 3 4 5 . . . n
𝒂 𝒏 5 12 19 26 33 . . . ?

4. GET THE DIFFERENCE
𝟓, 𝟏𝟐, 𝟏𝟗, 𝟐𝟔, 𝟑𝟑, …
𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝟕

5. SOLVE FOR a AND b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟓
𝑎 1 + 𝑏 = 5
𝒂 + 𝒃 = 𝟓 𝑬𝒒. 𝟏
𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟏𝟐
𝑎 2 + 𝑏 = 12
𝟐𝒂 + 𝒃 = 𝟏𝟐 𝑬𝒒. 𝟐

6. 𝒂 + 𝒃 = 𝟓 𝑬𝒒. 𝟏
𝟐𝒂 + 𝒃 = 𝟏𝟐 𝑬𝒒. 𝟐
𝒂 = 𝟕
𝒂 + 𝒃 = 𝟓 𝑬𝒒. 𝟏
𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂.
𝟕 + 𝒃 = 𝟓
𝒃 = 𝟓 − 𝟕
𝒃 = −𝟐
SOLVE FOR a AND b.
𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐

7. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝟕𝒏 − 𝟐 = 𝒂 𝒏
𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆
𝟓, 𝟏𝟐, 𝟏𝟗, 𝟐𝟔, 𝟑𝟑, . . . is
𝒂 𝒏 = 𝟕𝐧 − 𝟐

8. EXAMPLE:
FIND THE GENERAL TERM OF
THE SEQUENCE
7, 11, 15, 19, 23, . . .

9. PREPARE A TABLE
n 1 2 3 4 5 . . . n
𝒂 𝒏 7 11 15 19 23 . . . ?

10. GET THE DIFFERENCE
𝟕, 𝟏𝟏, 𝟏𝟓, 𝟏𝟗, 𝟐𝟑, …
𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝟒

11. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟕
𝑎 1 + 𝑏 = 7
𝒂 + 𝒃 = 𝟕 𝑬𝒒. 𝟏
𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟏𝟏
𝑎 2 + 𝑏 = 11
𝟐𝒂 + 𝒃 = 𝟏𝟏 𝑬𝒒. 𝟐

12. 𝒂 + 𝒃 = 𝟕 𝑬𝒒. 𝟏
𝟐𝒂 + 𝒃 = 𝟏𝟏 𝑬𝒒. 𝟐
𝒂 = 𝟒
𝒂 + 𝒃 = 𝟕 𝑬𝒒. 𝟏
𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂.
𝟒 + 𝒃 = 𝟕
𝒃 = 𝟕 − 𝟒
𝒃 = 𝟑
SOLVE FOR a AND b.
𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐

13. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝟒𝒏 + 𝟑 = 𝒂 𝒏
𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆
𝟓, 𝟏𝟐, 𝟏𝟗, 𝟐𝟔, 𝟑𝟑, . . . is
𝒂 𝒏 = 𝟒𝐧 + 𝟑

14. QUIZ:
1. FIND THE GENERAL
TERM OF THE SEQUENCE
1, 3, 5, 7, 9, . . .
2. FIND THE GENERAL
TERM OF THE SEQUENCE
-2, 1, 4, 7, 10, . . .
3. FIND THE GENERAL
TERM OF THE SEQUENCE
-1, 1, 3, 5, 7, 9, . . .

15. QUIZ:
FIND THE GENERAL TERM OF
THE SEQUENCE
1, 3, 5, 7, 9, . . .

16. PREPARE A TABLE
n 1 2 3 4 5 . . . n
𝒂 𝒏 1 3 5 7 9 . . . ?

17. GET THE DIFFERENCE
𝟏, 𝟑, 𝟓, 𝟕, 𝟗, …
𝒂𝒏 + 𝒃 = 𝒂 𝒏
2

18. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟏
𝑎 1 + 𝑏 = 1
𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟏
𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟑
𝑎 2 + 𝑏 = 3
𝟐𝒂 + 𝒃 = 𝟑 𝑬𝒒. 𝟐

19. 𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟏
𝟐𝒂 + 𝒃 = 𝟑 𝑬𝒒. 𝟐
𝒂 = 𝟐
𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟏
𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂.
𝟐 + 𝒃 = 𝟏
𝒃 = 𝟏 − 𝟐
𝒃 = −𝟏
SOLVE FOR a AND b.
𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐

20. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝟐𝒏 − 𝟏 = 𝒂 𝒏
𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆
𝟏, 𝟑, 𝟓, 𝟕, 𝟗, . . . is
𝒂 𝒏 = 𝟐𝐧 − 𝟏

21. QUIZ:
FIND THE GENERAL TERM OF
THE SEQUENCE
-2, 1, 4, 7, 10, . . .

22. PREPARE A TABLE
n 1 2 3 4 5 . . . n
𝒂 𝒏 -2 1 4 7 10 . . . ?

23. GET THE DIFFERENCE
−𝟐, 𝟏, 𝟒, 𝟕, 𝟏𝟎, …
𝒂𝒏 + 𝒃 = 𝒂 𝒏
3

24. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = −𝟐
𝑎 1 + 𝑏 = −2
𝒂 + 𝒃 = −𝟐 𝑬𝒒. 𝟏
𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟏
𝑎 2 + 𝑏 = 1
𝟐𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟐

25. 𝒂 + 𝒃 = −𝟐 𝑬𝒒. 𝟏
𝟐𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟐
𝒂 = 𝟑
𝒂 + 𝒃 = −𝟐 𝑬𝒒. 𝟏
𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂.
𝟑 + 𝒃 = −𝟐
𝒃 = −𝟐 − 𝟑
𝒃 = −𝟓
SOLVE FOR a AND b.
𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐

26. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝟑𝒏 − 𝟓 = 𝒂 𝒏
𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆
−𝟐, 𝟏, 𝟒, 𝟕, 𝟏𝟎, . . . is
𝒂 𝒏 = 𝟑𝐧 − 𝟓

27. QUIZ:
FIND THE GENERAL TERM OF
THE SEQUENCE
-1, 1, 3, 5, 7, 9, . . .

28. PREPARE A TABLE
n 1 2 3 4 5 . . . n
𝒂 𝒏 -1 1 3 5 7 . . . ?

29. GET THE DIFFERENCE
−𝟏, 𝟏, 𝟑, 𝟓, 𝟕, 𝟗, …
𝒂𝒏 + 𝒃 = 𝒂 𝒏
2

30. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = −𝟏
𝑎 1 + 𝑏 = −1
𝒂 + 𝒃 = −𝟏 𝑬𝒒. 𝟏
𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟏
𝑎 2 + 𝑏 = 1
𝟐𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟐

31. 𝒂 + 𝒃 = −𝟏 𝑬𝒒. 𝟏
𝟐𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟐
𝒂 = 𝟐
𝒂 + 𝒃 = −𝟏 𝑬𝒒. 𝟏
𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂.
𝟐 + 𝒃 = −𝟏
𝒃 = −𝟏 − 𝟐
𝒃 = −𝟑
SOLVE FOR a AND b.
𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐

32. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝟐𝒏 − 𝟑 = 𝒂 𝒏
𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆
−𝟏, 𝟏, 𝟑, 𝟓, 𝟕, 𝟗, . . . is
𝒂 𝒏 = 𝟐𝐧 − 𝟑

33. ASSIGNMENT!
FIND THE GENERAL TERM OF THE FOLLOWING.
1. 3, 7, 11, 15, . . .
2. 2, 6, 10, 14, . . .
3. 5, 11, 17, 23, . . .
4. 9, 11, 13, 15, . . .
5. -2, -5, -8, -11, . . .

34. ASSIGNMENT:
FIND THE GENERAL TERM OF
THE SEQUENCE
1. 3, 7, 11, 15, . . .

35. PREPARE A TABLE
n 1 2 3 4 5 . . . n
𝒂 𝒏 3 7 11 15 . . . ?

36. GET THE DIFFERENCE
𝟑, 𝟕, 𝟏𝟏, 𝟏𝟓, …
𝒂𝒏 + 𝒃 = 𝒂 𝒏
4

37. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟑
𝑎 1 + 𝑏 = 3
𝒂 + 𝒃 = 𝟑 𝑬𝒒. 𝟏
𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟕
𝑎 2 + 𝑏 = 7
𝟐𝒂 + 𝒃 = 𝟕 𝑬𝒒. 𝟐

38. 𝒂 + 𝒃 = 𝟑 𝑬𝒒. 𝟏
𝟐𝒂 + 𝒃 = 𝟕 𝑬𝒒. 𝟐
𝒂 = 𝟒
𝒂 + 𝒃 = 𝟑 𝑬𝒒. 𝟏
𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂.
𝟒 + 𝒃 = 𝟑
𝒃 = 𝟑 − 𝟒
𝒃 = −𝟏
SOLVE FOR a AND b.
𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐

39. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝟒𝒏 − 𝟏 = 𝒂 𝒏
𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆
𝟑, 𝟕, 𝟏𝟏, 𝟏𝟓, . . . is
𝒂 𝒏 = 𝟒𝐧 − 𝟏

40. ASSIGNMENT:
FIND THE GENERAL TERM OF
THE SEQUENCE
2. 2, 6, 10, 14, . . .

41. PREPARE A TABLE
n 1 2 3 4 5 . . . n
𝒂 𝒏 2 6 10 14 . . . ?

42. GET THE DIFFERENCE
𝟐, 𝟔, 𝟏𝟎, 𝟏𝟒, . . .
𝒂𝒏 + 𝒃 = 𝒂 𝒏
4

43. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟐
𝑎 1 + 𝑏 = 2
𝒂 + 𝒃 = 𝟐 𝑬𝒒. 𝟏
𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟔
𝑎 2 + 𝑏 = 6
𝟐𝒂 + 𝒃 = 𝟔 𝑬𝒒. 𝟐

44. 𝒂 + 𝒃 = 𝟐 𝑬𝒒. 𝟏
𝟐𝒂 + 𝒃 = 𝟔 𝑬𝒒. 𝟐
𝒂 = 𝟒
𝒂 + 𝒃 = 𝟐 𝑬𝒒. 𝟏
𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂.
𝟒 + 𝒃 = 𝟐
𝒃 = 𝟐 − 𝟒
𝒃 = −𝟐
SOLVE FOR a AND b.
𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐

45. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝟒𝒏 − 𝟐 = 𝒂 𝒏
𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆
𝟐, 𝟔, 𝟏𝟎, 𝟏𝟒, . . . is
𝒂 𝒏 = 𝟒𝐧 − 𝟐

46. ASSIGNMENT:
FIND THE GENERAL TERM OF
THE SEQUENCE
3. 5, 11, 17, 23, . . .

47. PREPARE A TABLE
n 1 2 3 4 5 . . . n
𝒂 𝒏 5 11 17 23 . . . ?

48. GET THE DIFFERENCE
𝟓, 𝟏𝟏, 𝟏𝟕, 𝟐𝟑, . . .
𝒂𝒏 + 𝒃 = 𝒂 𝒏
6

49. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟓
𝑎 1 + 𝑏 = 5
𝒂 + 𝒃 = 𝟓 𝑬𝒒. 𝟏
𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 𝟏𝟏
𝑎 2 + 𝑏 = 11
𝟐𝒂 + 𝒃 = 𝟏𝟏 𝑬𝒒. 𝟐

50. 𝒂 + 𝒃 = 𝟓 𝑬𝒒. 𝟏
𝟐𝒂 + 𝒃 = 𝟏𝟏 𝑬𝒒. 𝟐
𝒂 = 𝟔
𝒂 + 𝒃 = 𝟓 𝑬𝒒. 𝟏
𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂.
𝟔 + 𝒃 = 𝟓
𝒃 = 𝟓 − 𝟔
𝒃 = −𝟏
SOLVE FOR a AND b.
𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐

51. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝟔𝒏 − 𝟏 = 𝒂 𝒏
𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆
𝟓, 𝟏𝟏, 𝟏𝟕, 𝟐𝟑, . . . is
𝒂 𝒏 = 𝟔𝐧 − 𝟏

52. ASSIGNMENT:
FIND THE GENERAL TERM OF
THE SEQUENCE
4. 9, 11, 13, 15, . . .

53. PREPARE A TABLE
n 1 2 3 4 5 . . . n
𝒂 𝒏 9 11 13 15 . . . ?

54. GET THE DIFFERENCE
𝟗, 𝟏𝟏, 𝟏𝟑, 𝟏𝟓, . . .
𝒂𝒏 + 𝒃 = 𝒂 𝒏
2

55. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟗
𝑎 1 + 𝑏 = 9
𝒂 + 𝒃 = 𝟗 𝑬𝒒. 𝟏
𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 𝟏𝟏
𝑎 2 + 𝑏 = 11
𝟐𝒂 + 𝒃 = 𝟏𝟏 𝑬𝒒. 𝟐

56. 𝒂 + 𝒃 = 𝟗 𝑬𝒒. 𝟏
𝟐𝒂 + 𝒃 = 𝟏𝟏 𝑬𝒒. 𝟐
𝒂 = 𝟐
𝒂 + 𝒃 = 𝟗 𝑬𝒒. 𝟏
𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂.
𝟔 + 𝒃 = 𝟗
𝒃 = 𝟗 − 𝟔
𝒃 = 𝟕
SOLVE FOR a AND b.
𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐

57. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝟐𝒏 + 𝟕 = 𝒂 𝒏
𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆
𝟗, 𝟏𝟏, 𝟏𝟑, 𝟏𝟓, . . . is
𝒂 𝒏 = 𝟐𝐧 + 𝟕

58. ASSIGNMENT:
FIND THE GENERAL TERM OF
THE SEQUENCE
5. -2, -5, -8, -11, . . .

59. PREPARE A TABLE
n 1 2 3 4 5 . . . n
𝒂 𝒏 -2 -5 -8 -11 . . . ?

60. GET THE DIFFERENCE
−𝟐, −𝟓, −𝟖, −𝟏𝟏, . . .
𝒂𝒏 + 𝒃 = 𝒂 𝒏
−3

61. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = −𝟐
𝑎 1 + 𝑏 = −2
𝒂 + 𝒃 = −𝟐 𝑬𝒒. 𝟏
𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = −𝟓
𝑎 2 + 𝑏 = −5
𝟐𝒂 + 𝒃 = −𝟓 𝑬𝒒. 𝟐

62. 𝒂 + 𝒃 = −𝟐 𝑬𝒒. 𝟏
𝟐𝒂 + 𝒃 = −𝟓 𝑬𝒒. 𝟐
𝒂 = −𝟑
𝒂 + 𝒃 = −𝟐 𝑬𝒒. 𝟏
𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂.
−𝟑 + 𝒃 = −𝟐
𝒃 = −𝟐 + 𝟑
𝒃 = 𝟏
SOLVE FOR a AND b.
𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐

63. 𝒂𝒏 + 𝒃 = 𝒂 𝒏
−𝟑𝒏 + 𝟏 = 𝒂 𝒏
𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆
−𝟐, −𝟓, −𝟖, −𝟏𝟏, . . . is
𝒂 𝒏 = 𝟏 − 𝟑𝐧