Download presentation

Presentation is loading. Please wait.

Published byTerrance Harbinson Modified over 3 years ago

1
Unit 1 Outcome 4 Recurrence Relations Sequences A591317……. B361224……. C235813…….. D17234177137……… E235711……… In the above sequences some have obvious patterns while others don’t however this does not mean that a pattern doesn’t exist.

2
Notation Suppose we write the terms of a sequence as u 1, u 2, u 3, …….., u n-1, u n, u n+1, ……... where u 1 is the 1 st term, u 2 is the 2 nd term etc…. and u n is the n th term ( n being any whole number.) The terms of a sequence can then be defined in two ways

3
Either Using a formula for the nth term, u n, in terms of the value n. Or By expressing each term using the previous term(s) in the sequence. This is called a Recurrence Relation. Now reconsider the sequences at the start

4
A591317……. Formula: u n = 4n + 1 So u 100 = 4 X 100 + 1 = 401 Recurrence Relation: u n+1 = u n + 4 with u 1 = 5 So u 2 = u 1 + 4 = 5 + 4 = 9, u 3 = u 2 + 4 = 9 + 4 = 13, etc

5
B361224……. Formula: u n = 3 X 2 n-1 So u 10 = 3 X 2 9 = 3 X 512 = 1536 Recurrence Relation: u n+1 = 2u n with u 1 = 3. So u 2 = 2u 1 = 2 X 3 = 6, u 3 = 2u 2 = 2 X 6 = 12, etc

6
C235813…….. No formula this time but we have a special type of recurrence relation called a FIBONACCI SEQUENCE. Here u 1 = 2, u 2 = 3 then we have u 3 = u 2 + u 1 = 3 + 2 = 5, u 4 = u 3 + u 2 = 5 + 3 = 8, etc In general u n+2 = u n+1 + u n ie apart from 1st two, each term is the sum of the two previous terms.

7
D17234177137……… This sequence doesn’t have a recurrence relation but the terms can be found using the formula u n = n 3 - n + 17 Quite a tricky formula but it does work... u 1 = 1 3 - 1 + 17 = 17 u 2 = 2 3 - 2 + 17 = 8 - 2 + 17 = 23 etc Also u 10 = 10 3 - 10 + 17 = 1000 - 10 + 17 = 1007

8
E235711……… This sequence is the PRIME NUMBERS (NB: Primes have exactly two factors !!) There is neither a formula nor a recurrence relation which will give us all the primes.

Similar presentations

OK

Numbers and Operations on Numbers. Numbers can represent quantities, amounts, and positions on a number line. The counting numbers (1, 2, 3, 4, 5…) are.

Numbers and Operations on Numbers. Numbers can represent quantities, amounts, and positions on a number line. The counting numbers (1, 2, 3, 4, 5…) are.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on interview etiquettes of life Ppt on no plastic bags Ppt on internal auditing process approach Ppt on limits and derivatives in calculus Ppt on architecture of mughal period Ppt on cross cultural communication barriers Ppt on email etiquettes presentation ideas Ppt on column chromatography separation Ppt on question tags games Ppt on kinds of dependent clauses