Chapter 8: Sequence, Series and Probability

1. Find the first three terms of the sequence:

a) {1 - 2n} b) {9} c) {1 + nⁿ}

Arithmetic Sequence of the nth Term

a _n = a ₁ + (n - 1)d

Example: The first three terms of an arithmetic sequence are 1, 1.5, and 2.

Find the 5^th term.

Solution: The difference is 1.5 - 1.0 = 0.5

a ₁ = 1, d = 0.5, and n = 5 in a _n = a ₁ + (n - 1)d is 3.

2. Find the 5^th and 10^th term of arithmetic sequence:

a) 1, 5, 9, 18,...

b) x - 8, x - 3, x + 2, x + 7,...

c) -5, -3.5, -2, -0.5,...

Geometric Sequence of the nth Term

a _n = a ₁ r ^n-1

3. Find the 5^th and 10^th term of geometric sequence:

a) 200, -20, 2, -0.2,...

b) 4, -6, 9, -13.5,...

d) 3, 3^x+1, 3^2x+1, 3^3x+1,...

Definition of the Probability of an Event

Let S be the sample space of an experiment and E an event. The probability P(E) of E is given by

P(E) = n(E)/n(S)

4. A 6-member committee is to be chosen by drawing names of individuals form a hat. If the hat contains the names of 8 men and 14 women, find the probability that the committee will consist of 3 men and 3 women.

5.

The figure above is a small version of a probability demonstration device. A

small ball is dropped into the top of the maze and tumbles to the bottom.

Each time the ball strikes an obstacle, there is a 50% chance that the ball will

move to the left. Find the probability that the ball ends up in a slot.