Number Patterns

Question 1

What is the general formula for a linear sequence/pattern?

Answer 1

Tn = a + (n - 1)d

Question 2

What does the n and d represent in the linear sequence equation?

Answer 2

n represents the term number
d represents the difference between two consecutive terms

Question 3

What is the general formula for a quadratic sequence?

Answer 3

Tn = an^2 + bn + c

Question 4

How do you identify a quadratic sequence?

Answer 4

The second difference is constant.

Question 5

What are the three expressions used to determine a, b and c in a quadratic sequence?

Answer 5

2a
3a + b
a + b + c

Question 6

How do you determine the term number of a given value in any sequence?

Answer 6

Substitute the given value as Tn and then solve for n

Question 7

How do you solve for a in a quadratic sequence

Answer 7

2a = second difference. You then solve for a

Question 8

How do you solve for b in a quadratic sequence?

Answer 8

3a + b = first first difference. Solve for a first, then solve for b

Question 9

How do you solve for c in a quadratic sequence?

Answer 9

Solve for a and b first.
a + b + c = first term. Solve for c

Question 10

How do you determine the value of a certain term number in any sequence?

Answer 10

Substitute the term number in the appropriate equation and simplify.