Chapter 9 - Part 1 - Sequences

Question 1

State the square numbers up to 5 squared

Answer 1

1, 4, 9, 16, 25

Question 2

State the cube numbers up to 5 cubed

Answer 2

1, 8, 27, 64, 125

Question 3

State the triangular numbers up to the 5th one & what is the formula

Answer 3

1, 3, 6, 10, 15…
1/2n(n+1)

Question 4

State the Fibonacci sequence up to 21 & what is it

Answer 4

• the Fibonacci sequence is a sequence in which you add the 2 previous terms together to get one next term
  1, 1, 2, 3, 5, 8, 13, 21…

Question 5

What is an arithmetic sequence & what is the formula

Answer 5

• a list of numbers in which the difference between consecutive terms is constant
• aₙ = a₁ + (n – 1)d

Question 6

What is a geometric sequence and what is the formula

Answer 6

• a geometric sequence is when the relation between terms is defined as each term is formed by multiplying the previous term with a constant number
• aₙ = a₁ x r ⁽ⁿ⁻¹⁾
  (a on the right is the first term and r is what the sequence increases by)

Question 7

What are quadratic sequences and what is the formula

Answer 7

• quadratic sequences are a sequence of numbers in which the second difference between any two terms is constant
• you need to use 4 steps to find out the term to term rule
  - second difference —> 2a (a is dif)
  - first difference —> 3a + b = first term of first difference
  - a + b + c = first term
  - substitute answers —> aₙ = an² + bn + c

Question 8

What is a rational number

Answer 8

Any number that can be expressed as a fraction in it’s lowest term

Question 9

Empty ??

Question 10

How do you convert decimals to fractions