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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 100th and the 90th 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

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