Cambridge International AS and A Level Mathematics Pure Mathematics 1

Sequences and series

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18 As part of a fund-raising campaign, I have

been given some books of raffle tickets to sell.

Each book has the same number of tickets

and all the tickets I have been given are

numbered in sequence. The number of the

ticket on the front of the 5th book is 205 and

that on the front of the 19th book is 373.

(i) By writing the number of the ticket on the front of the first book as a

and the number of tickets in each book as d, write down two equations

involving a and d.

(ii) From these two equations find how many tickets are in each book and

the number on the front of the first book I have been given.

(iii) The last ticket I have been given is numbered 492.

How many books have I been given?

[MEI]

Geometric progressions

A human being begins life as one cell, which divides into two, then four....

The terms of a geometric sequence are formed by multiplying one term by a fixed

number, the common ratio, to obtain the next. This can be written inductively as:

uk+1 = ruk with first term u 1.

The sum of the terms of a geometric sequence is called a geometric progression,

shortened to G.P. An alternative name is a geometric series.

Notation

When describing geometric sequences in this book, the following conventions

are used:

●●first term u 1 = a

●●common ratio = r

(^206207)
Geometric progressions
Figure 3.2