Number patterns

Question 1

Linear sequence general term equation

Answer 1

Tn = a + (n - 1)d

Question 2

Quadratic sequence general term equation

Answer 2

Tn = an^2 + bn + c

Question 3

How do you check whether a sequence is arithmetic or not?

Answer 3

Check if the difference between any two consecutive terms is constant

Question 4

How do you check whether a sequence is quadratic or not?

Answer 4

Check if the second difference between any two consecutive terms is constant

Question 5

How do you obtain the constant ratio in a geometric sequence

Answer 5

Divide any two consecutive terms, with the term on the right being the numerator and the term on the left being the denominator.

Question 6

What are the 3 expressions used to find the variables a, b and c in a quadratic sequence

Answer 6

2a
3a + b
a + b + c

Question 7

What do the letters a, d, r and n refer to in the equations of number patterns

Answer 7

a refers to the first term
d refers to the common difference
r refers to the common ratio
n refers to the term number

Question 8

For what values of r does a geometric series converge?

Answer 8

For values between -1 and 1.

Question 9

What is meant by a converging series?

Answer 9

A series that approaches a certain limit as the number of terms increases.

Question 10

What is the difference between a sequence and a series

Answer 10

A sequence is a set of ordered numbers while a series is a set of ordered numbers added together.