A RI THM ETIC PROGR ESSIONG EO METR ICSERIES
51 is the 6th pentagonal number.
What is the 100th pentagonal number?
Session content
Sequences
Recurrence relations
Sigma notation
Arithmetic Progressions
Geometric Progressions
NB: This is content based on chapter 7 in the AS Core textbook
Arithmetic Progressions & Series
1 2 3 1
100
100
1001
1, 4, 7, ... 3
1 99 3 298
n n
rr
u u u u u
u
S u
Typical APs Exam Question (Core 2 Jan 07 - Q8 [5 marks])The 7th term of an arithmetic progression is 6.
The sum of the first 10 terms of the progression is 30.
Find the 5th term of the progression.
1 17 8 10 11
2 2
2 5 8 11
1 1.1 1.2 1.3
1 1.1 1.11 1.111
1 5 7 3
2 6 6 2
2 2 2 21 2 3 4
2 3 4n n n n 1 1 1
12 3 4
1 1 1 1
2 3 4a a a a
1 1.1 1.21 1.331
1 1 1 1
2 6 12 36
2 4 8 16
3 927 162
4 2
AP or GP?
Typical GPs Exam Question
Find two different geometric progressions with second term 18 and fourth term 2.
Find the sum of the first 100 terms in each case.
Sum to infinity of a geometric series2 3 10
2 3 100
2 3
1 1 1 1...
4 4 4 4
1 1 1 1...
4 4 4 4
1 1 1...
4 4 4
Typical Infinite GPs Exam Question(Core 2 Jan 08 - Q8 [5 marks]) The second term of a geometric progression is 18 and the fourth term is 2. The common ratio is positive. Find the sum to infinity of this progression.
Session content check
Sequences
Recurrence relations
Sigma notation
Arithmetic Progressions
Geometric Progressions
MEI Core 2 Jun 08 - Q8 [5 marks]The 11th term of an arithmetic progression is 1. The sum of the first ten terms is 120. Find the 4th term.