More on finding the nth term

So the sequence of numbers in the {5} times table has a common difference of 5 and an {n}^{th} term of 5n.

Linear sequence diagram

How do you find the answer in more complex sequences?

Linear sequence diagram

We know that the {n}^{th} term should contain ‘ {5n}’.

The {5} times table is {5},~{10},~{15}, ...

The sequence is {7},~{12},~{17}, ...

Each term in the sequence is {2} more than the corresponding term in the {5} times table, so the n^{th} term is 5n + 2.

Question

What is the n^{th} term of the sequence {8},~{11},~{14}, ... ?

Linear sequence diagram

The common difference is 3, so it must be related to the 3 times table ( 3n).

The 3 times table is {3},~{6},~{9}, ...

The sequence is {8},~{11},~{14}, ...

Every term in the sequence is 5 more than the corresponding term in the 3 times table, so the {n}^{th} term is 3n + 5.

Move on to Video
next