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High School Mathematics - 23.1 Sequences and Series

 Sequence: A sequence is a number pattern in a definite order following a certain rule. Examples of sequences: 1, 2, 3, 4, 5, 6, 7, ... add 1 to the preceding term 2, 4, 7, 11, 16, 23, 31..... add 2 to the preceding term, -6, -3, 0, 3, 6,...... add 3 to the preceding term 1, 1, 2, 3, 5, 8, 13, 21, 34,... add the two preceding terms together The last sequence is known as the Fibonacci sequence, discovered by Leonardo of Pisa. This sequence occurs in nature, and Leonardo of Pisa derived it by studying the mating patterns of rabbits. Sequences are denoted by: a1, a2, a3, a4, a5 ..........an-1,an Series: Series is a sum of terms in a sequence. It can be denoted by: a1 + a2 + a3 + a4 + a5 ..........an-1 + an Using the above sequences, we have the following series: 1 + 2 + 3 + 4 + 5 + 6 + 7 +.............. 2 + 4 + 7 + 11 + 16 + 23 + 31. -6 + -3 + 0 + 3 + 6 +...... 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 +.................. Directions: Solve the following problems. Also write at least 5 examples of your own.
 Q 1: _____________ is a sum of a number each of which, after the first, is obtained by adding to the preceding number a constant number called the common differenceGeometric SeriesArithmetic series Q 2: Arithmetic sequence have a common _______. ratiodifference Q 3: A series is formed by the sum of the terms of a sequence.TrueFalse Q 4: The numbers in the sequence are called _______. termsvariablesexamples Q 5: Geometric sequence have a common _______. ratiodifference Q 6: 1 + 3 + 5 + 7 +... SeriesSequence Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!