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High School Mathematics - 2
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.