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. |

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