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High School Mathematics - 2
3.1 Sequences and Series

Sequence:
  • A sequence is a number pattern in a definite order following a certain rule.
  • Examples of sequences:
    1. 1, 2, 3, 4, 5, 6, 7, ... add 1 to the preceding term
    2. 2, 4, 7, 11, 16, 23, 31..... add 2 to the preceding term,
    3. -6, -3, 0, 3, 6,...... add 3 to the preceding term
    4. 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. 1 + 2 + 3 + 4 + 5 + 6 + 7 +..............
    2. 2 + 4 + 7 + 11 + 16 + 23 + 31.
    3. -6 + -3 + 0 + 3 + 6 +......
    4. 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: Geometric sequence have a common _______.
difference
ratio

Q 2: _____________ 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 difference
Arithmetic series
Geometric Series

Q 3: Arithmetic sequence have a common _______.
ratio
difference

Q 4: _____________ is a sum of a number each of which, after the first, is obtained by multiplying the preceding number by a constant number called common ratio.
Geometric series
Arithmetic series

Q 5: The numbers in the sequence are called _______.
terms
examples
variables

Q 6: 1,3,5,7,...
Sequence
Series

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Question 8: This question is available to subscribers only!


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