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### High School Mathematics - 23.8 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 geometric Series:1+2+3+4+5+.........34 + 41 + 48 + 55 + 62 +........2 + 6 + 18 + 54 + ....... Q 2: Which of the following is arithmetic Series:1+3+6+10+15+........1+2+3+4+5+.........3+6+12+24+48+............. Q 3: Which of the following is geometric Series:1+2+3+4+5+.........3+6+12+24+48+.............34 + 41 + 48 + 55 + 62 +........ Q 4: Which of the following is arithmetic Series:34 + 41 + 48 + 55 + 62 +........2 + 6 + 18 + 54 + ........1 + 2 + 4 + 8 + ............ Q 5: Which of the following is arithmetic Sequence:(-5),(-3),(-1),1,3,.......1/2 , 3/4 , 7/8 , 15/16 , 31/32 , 63/64-1,4,7,10,13,16,........ Q 6: Lisa's mother gives her 10 cents one day. Every day thereafter her mother gives her 5 more cents than the previous day. After 20 days how much does she have? This simple problem exhibits ____________series. (Hint: The series can be written as 10, 15,20,25,30........)GeometricArithmetic Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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