Topic 1: Number and Algebra

Topic 1 is mostly about arithmetic and geometric sequences. Those two have multiple concepts, and it is important to be familiar with the different cases in which arithmetic and geometric sequences are used for.

Arithmetic Sequences:

• The formula for the Arithmetic sequence is u = u + (n - 1)(d)

  • u is the value of the term n

  • u is the first number in the sequence

  • n is the number of the term

  • d is the common difference

• One of the most prominent cases for arithmetic sequences is when the common difference is not given and the given terms do not include the value of the first term. Ex: u6 = -5 and u9 = - 20 , find u20

  • To solve this case first you need to use the lower term as the first term and the higher term as the value of term n. The n is equal to the difference between the term numbers.

    • u9 = u6 + (9 - 6) (d)

  • Then sub in the values of the terms and solve for the common difference

    • - 20 = - 5 + (3)(d)

    • d = -15/3

    • d = -5

  • Now repeat the first step, but now use the term you are trying to find as the higher term

    • u20 = u6 + (20-6)(-5)

    • u20 = -5 + (14)(-5)

    • u20 = - 75

Arithmetic Series:

• The formula for the Arithmetic series is S = n/2 (u + u) or S = n/2 [2u + (n - 1)(d)]

  • The first formula is used when the common difference is not given

  • The second formula is used for other cases