Sequences and Series Questions

1. A geometric series has first term 1200. Its sum to infinity is 960.

(a) Show that the common ratio of the series is −41 .

(b) Find, to 3 decimal places, the difference between the ninth and tenth terms of the series.

(c) Write down an expression for the sum of the first n terms of the series.

(d) Given that n is an odd number, prove that the sum of the first n terms of the series is

960(1 + 0.25n)

2. The first term of a geometric series is a. The fourth and fifth terms of the series are 12 and –8

respectively.

(a) Find the value of the common ration of the series.

(b) Show that a = –4021 .

3. (a) A company made a profit of £54 000 in the year 2001. A model for future performance

assumes that yearly profits will increase in an arithmetic sequence with common difference £d.

This model predicts total profits of £619 200 for the 9 years 2001 to 2009 inclusive.

(i) Find the value of d.

Using your value of d,

(ii) find the predicted profit for the year 2011.

An alternative model assumes that the company’s yearly profits will increase in a geometric

sequence with common ratio 1.06. Using this alternative model and again taking the profit in

2001 to be £54 000,

(iii) find the predicted profit for the year 2011.

Sequences and Series Solutions

1. (b) 0.023

(c) S n =

( )( )( )

1200 1 025

1 025

− −

− −

.

.

n

2. (a) 3

2−

3. (i) 3700

(ii) 91 000

(iii) 96 700