Arithmetic Sequences and Series
1.	The first three terms of an arithmetic sequence are 7, 9.5, 12.
(a)	What is the 41st term of the sequence?
(b)	What is the sum of the first 101 terms of the sequence?
(Total 4 marks)

2.	In an arithmetic sequence, the first term is 5 and the fourth term is 40. Find the second term.
(Total 4 marks)

3.	In an arithmetic sequence, S40 = 1900 and u40 = 106. Find the value of u1 and of d.
(Total 6 marks)

4.	The nth term of an arithmetic sequence is given by un = 5 + 2n.
(a)	Write down the common difference.
(1)
 
(b)	(i)	Given that the nth term of this sequence is 115, find the value of n.
(ii)	For this value of n, find the sum of the sequence.
(5)
(Total 6 marks)

5.	In an arithmetic series, the first term is –7 and the sum of the first 20 terms is 620.
(a)	Find the common difference.
(3)
 
(b)	Find the value of the 78th term.
(2)
(Total 5 marks)

6.	Find the sum of the arithmetic series
17 + 27 + 37 +...+ 417.
(Total 4 marks)

7.	In an arithmetic sequence u1 = 7, u20 = 64 and un = 3709.
(a)	Find the value of the common difference.
(3)
 
(b)	Find the value of n.
(2)
(Total 5 marks)

Geometric Sequences and Series
8.	The first three terms of an infinite geometric sequence are 32, 16 and 8.
(a)	Write down the value of r.
(1)
 
(b)	Find u6.
(2)
 
(c)	Find the sum to infinity of this sequence.
(2)
(Total 5 marks)

9.	The first four terms of a sequence are 18, 54, 162, 486.
(a)	Use all four terms to show that this is a geometric sequence.
(2)
 
(b)	(i)	Find an expression for the nth term of this geometric sequence.
(ii)	If the nth term of the sequence is 1062 882, find the value of n.
(4)
(Total 6 marks)

10.	Find the sum of the infinite geometric series

(Total 4 marks)

11.	The first term of an infinite geometric sequence is 18, while the third term is 8. There are two possible sequences. Find the sum of each sequence.

(Total 6 marks)

12.	Consider the infinite geometric series 405 + 270 + 180 +....
(a)	For this series, find the common ratio, giving your answer as a fraction in its simplest form.
(b)	Find the fifteenth term of this series.
(c)	Find the exact value of the sum of the infinite series.
(Total 6 marks)

Complete all of the previous problems and check your solutions before moving on to Sigma Notation

Sigma Notation 
13. (a)	Expand  as the sum of four terms.
(1)
 
(b)	(i)	Find the value of .
(ii)	Explain why  cannot be evaluated.
(6)
(Total 7 marks)