# Exam-style Questions: Sequences and Series

**1.** A sequence u_{l}, u_{2}, u_{3},... is defined by

u_{l} = 10,

u_{n+l} = 0.9un.

**a)** Find the value of u_{4}

**b)** Find an expression for u_{n} in terms of n.

**c)** Find

**(Marks available: 5)**

**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 u_{1}, u_{2}, u_{3} and u_{4}, gives:

u_{4} = 7.29

**(1 mark)**

**b)** Using the series equation n^{th} term = ar^{n-1}, gives:

u_{n} = 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 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 n^{th} 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)**