# Creating a linear and quadratic sequence using the nth term formula.

Creating a sequence if given the nth term formula can be done by subbing in the numbers n=1, n=2, n=3, n=4, n=5... into the nth term formula.

Example 1

The nth term of a sequence is 3n + 2. Write down the first 5 numbers.

First make sure you understand the meaning of 3n + 2. It means to get the numbers in the sequence you need to multiply the position number by 3 and add on 2.

First of all sub in n = 1

3 × 1 + 2 = 5

Next sub n = 2

3 × 2 + 2 = 8

Next sub in n = 3

3 × 3 + 2 = 11

Next sub in n = 4

3 × 4 + 2 = 14

Finally, sub in n = 5

3 × 5 + 2 = 17

so the first 5 terms in the sequence are 5,8,11,14,17...

Example 2

The nth term of a sequence is 2n - 9. Write down the first 3 numbers.

First make sure you understand the meaning of 2n - 9. It means to get the numbers in the sequence you need to multiply the position number by 2 and take off 9.

First of all sub in n = 1

2 × 1 - 9 = -7

Next sub n = 2

2 × 2 - 9 = -5

Finally, sub in n = 3

2 × 3 - 9 = -3

so the first 3 terms in the sequence are -7,-5,-3...

Example 3

Find the first 5 terms of the sequence 3n² + 1

Quadratic sequence can be created in a similar way.

First of all sub in n = 1

3 × 1² + 1 = 5

Next sub n = 2

3 × 2² + 1 = 13

Next sub in n = 3

3 × 3² + 1 = 28

Next sub in n = 4

3 × 4² + 1 = 49

Finally, sub in n = 5

3 × 5² + 1 = 76

so the first 5 terms in the sequence are 5,13,28,49,76...

More help from me on sequences:

How to find the nth term of an increasing linear sequence.

Quadratic Sequences. The nth term of a quadratic number sequence.

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