Worksheet Chapter 1: Patterns and Sequences

1. Find the 8th term (T8) of the sequence: 5, 11, 17, 23, ...

2. Given the sequence 12, 7, 2, -3, -8, ..., state the pattern in words and write the next term.

3. Fill in the blank: A sequence of numbers where each term is obtained by adding the two preceding terms is called the ________ sequence.

4. The nth term of a sequence is given by Tn = 3n + 2. If Tn = 35, find the position n of this term.

5. True or False: The number 0 is the first term in Pascal's Triangle.

6. True or False: The general term for even numbers 2, 4, 6, 8, ... can be written as Tn = 2n, where n = 1, 2, 3, ...

7. Which of the following represents the 4th row of Pascal's Triangle?

8. A sequence is defined by the formula Tn = 4n - 3. Calculate the sum of the 3rd term and the 6th term.

9. Complete the missing terms x and y in the Fibonacci-style sequence where each term is the sum of the two preceding terms: 2, 5, x, 12, y, 31.

10. In a display of cans at a supermarket, the bottom row has 20 cans, the second row from bottom has 18 cans, the third has 16 cans, and so on. (a) Formulate the general algebraic term Tn for the number of cans in row n from the bottom. (b) Calculate the number of cans in the 7th row.