One of the questions that catches students out a lot when they are dealing with sequences is generating a sequence from an nth term.

To deal with this, we have to remember what an nth term is actually for. It is a position to term rule that allows the position within the sequence to give us the number in the sequence.

**Example 1: Find the first 5 terms in the sequence 4n - 6**

For this, we have to substitute in the values n = 1, n = 2, n = 3, n = 4 and n = 5 into the nth term.

When n = 1, 4n - 6 = (4 x **1**) - 6 = -2

When n = 2, 4n - 6 = (4 x **2**) - 6 = 2

When n = 3, 4n - 6 = (4 x **3**) - 6 = 6

When n = 4, 4n - 6 = (4 x **4**) - 6 = 10

When n = 5, 4n - 6 = (4 x **5**) - 6 = 14

So our first five terms for the sequence 4n - 6 are -2, 2, 6, 10, 14

**Example 2: Find the difference between the 100 ^{th} and the 90^{th} terms in the sequence 5n + 2 **

The approach to this is very similar to the last question but we use n = 90 and n = 100

When n = 100, 5n + 2 = (5 x **100**) +2 = 502

When n = 90, 5n + 2 = (5 x 90) +2 = 452

We can then find the difference by subtracting the two values. 502 - 450 = 50