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High School Mathematics - 2
3.8 Arithmetic or Geometric Series

Arithmetic series is defined by:
a + (a+d) + (a+2d) + (a+3d) + ..... + (a+(n-1)d) = n (2 a + (n - 1) d) / 2

Geometric series is defined by:
a + ar + ar2 + ar3 + ..... + arn-1 = a (1 - rn) / (1 - r), for r not equal to 1

Examples:
3, 8, 13, 18, 23, . . . arithmetic sequence with common value of 5
1, 2, 4, 8, 16, . . . . . geometric sequence with common ratio of 2
24, 12, 6, 3, 3/2, 3/4, . . geometric sequence with common ratio of 1/2
55, 51, 47, 43, 39, 35, . . . arithmetic sequence with common value of - 4
2, 5, 10, 17, . . . Neither arithmetic nor geometric
3, 11, 19, 27, 35, . . . arithmetic sequence with common value of 8
2/9, 2/3, 2, 6, 18, . . . geometric sequence with common ratio of 3
1, 3, 4, 7, 8, 11, . . . Neither arithmetic nor geometric
9, 6, 3, 0, -3, -6 . . . arithmetic sequence with common value of -3
9, 9, 9, 9, 9, 9 . . . either arithmetic or geometric with common value of 0 or common ratio of 1
1, 4, 9, 16, 25, 36, . . . Neither arithmetic nor geometric
-4, 1, 6, 11, 16, . . . arithmetic sequence with common value of 5
3, -3, 3, -3, 3, . . . geometric sequence with common ratio of -1

Directions: Answer the following questions. Also write at least 5 examples of your own.
Q 1: Which of the following is arithmetic Series:
1+3+6+10+15+........
3+6+12+24+48+.............
1+2+3+4+5+.........

Q 2: Which of the following is arithmetic Series:
2 + 6 + 18 + 54 + ........
1 + 2 + 4 + 8 + ............
34 + 41 + 48 + 55 + 62 +........

Q 3: Which of the following is geometric Series:
2 + 6 + 18 + 54 + .......
34 + 41 + 48 + 55 + 62 +........
1+2+3+4+5+.........

Q 4: Which of the following is geometric Series:
1+2+3+4+5+.........
34 + 41 + 48 + 55 + 62 +........
3+6+12+24+48+.............

Q 5: Which of the following is arithmetic Sequence:
1/2 , 3/4 , 7/8 , 15/16 , 31/32 , 63/64
(-5),(-3),(-1),1,3,.......
-1,4,7,10,13,16,........

Q 6: Which of the following is arithmetic Sequence:
2, 5, 10, 17, . . .
(1/2) , (-1) , 2 , (-4) , 8 , (-16) , 32.....
-5, -3,-1,1,3,..........

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Question 8: This question is available to subscribers only!


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