Number patterns

Question 3

Here is a sequence of 4 numbers.

3, 14, 58, 234

Give the rule for finding the next term from the previous term given that it is of the form:
Term 2 = Term 1 × n + 2
Term 3 = Term 2 × n + 2
Term 4 = Term 3 × n + 2
Where n is a fixed number.

Solution

Term 2 = Term 1 × n + 2
14 = 3 × n + 2
12 = 3n
n = 4.

Check:

Term 2: 3 × 4 + 2 = 14.

Term 3: 14 × 4 + 2 = 58.

Term 4: 58 × 4 + 2 = 234.

Question 2

Question 4