Exam-style Questions: Sequences and Series

1. A sequence ul, u2, u3,... is defined by

ul = 10,

un+l = 0.9un.

a) Find the value of u4

b) Find an expression for un in terms of n.

c) Find

Copyright S-cool

(Marks available: 5)

Answer

Answer outline and marking scheme for question: 1

Give yourself marks for mentioning any of the points below:

a) Simply placing calculating the values of u1, u2, u3 and u4, gives:

u4 = 7.29

(1 mark)

b) Using the series equation nth term = arn-1, gives:

un = 10(0.9)n-l

(2 marks)

c) Using the 'Sum to infinity' equation:

sum = a/(1-r)

Substituting in a and r, gives:

Sum to infinity = 100.

(2 marks)

(Marks available: 5)

2. Every year the Queen presents special coins (Maundy Money) to a number of selected people. The number of people receiving the coins in a year is equal to twice the Queen's age in years.

Given that in 1952, the first year of the Queen''s reign, her age was 26,

a) find an expression for the number of people receiving the coins in the nth year of her reign,

b) calculate the total number of people receiving the coins from 1952 to 1998 inclusive.

(Marks available: 6)

Answer

Answer outline and marking scheme for question: 2

Give yourself marks for mentioning any of the points below:

a) Use a + (n -1)d with a =52 and d=2 The nth term = 52 + 2(n - 1)

Any alternative methods leading to mn+c with, m = 2 and c = 50 is also acceptable.

(3 marks)

b) Establish that n = 47 (No of terms)

Use the equation Marks available: 1/2n x (2a +(n -1)d)

Therefore the No of people = 4606

(3 marks)

(Marks available: 6)