In the first part of this unit we consider sequences where the difference between successive terms is the same every time. We also use formulae to create the terms of a sequence.

Write down the next 3 terms of each of the following sequences:

(a)

7, 11, 15, 19, 23, ...

7 | 11 | 15 | 19 | 23 | ... |

4 | 4 | 4 | 4 |

7, 11, 15, 19, 23, 27, 31, 35

(b)

1, 9, 17, 25, 33, ...

1 | 9 | 17 | 25 | 33 | ... |

8 | 8 | 8 | 8 |

1, 9, 17, 25, 33, 41, 49, 57

A sequence is defined by the formula u_n = 3n + 1.

Calculate the first 5 terms of this sequence.

The first term, often called u_1, is formed by substituting

For the second term, substitute *n* = 2 to give:

For the third term, substitute *n* = 3 to give:

For the fourth term, substitute *n* = 4 to give:

For the fifth term, substitute *n* = 5 to give:

So the first 5 terms of the sequence are

4, 7, 10, 13, 16.

The terms of a sequence are given by the formula u_n = 8n – 3.

Calculate:

(a)

the first 3 terms of the sequence,

*n* = 1 gives u_1 = 8 × 1 – 3 = 5

*n* = 2 gives u_2 = 8 × 2 – 3 = 13

*n* = 3 gives u_3 = 8 × 3 – 3 = 21

So the first 3 terms are

5, 13, 21.

(b)

the 100th term of the sequence,

*n* = 100 gives u_100 = 8 × 100 – 3 = 797

So the 100th term of the sequence is 797.

(c)

the 200th term of the sequence.

*n* = 200 gives u_200 = 8 × 200 – 3 = 1597

So the 200th term of the sequence is 1597.