Question 1

For the sequence 2; 7; 14; 23; 34; ..., calculate the first differences (list all four).

Accepted Answer

5,7,9,11 — First differences: 7-2=5, 14-7=7, 23-14=9, 34-23=11.

Question 2

For the sequence 2; 7; 14; 23; 34; ... with first differences 5;7;9;11, what is the constant second difference?

Accepted Answer

2 — Second differences: 7-5=2, 9-7=2, 11-9=2, a constant value of 2.

Question 3

A sequence has first differences that are NOT constant, but its second differences ARE constant. What type of pattern is this?

Accepted Answer

A quadratic pattern — Non-constant first differences with constant second differences is the defining test for a quadratic pattern.

Number Patterns

Sample practice questions