Sequences

 

·       Formula for the nth term of a sequence

 

Calculate the first six terms of the sequence   

 

  

 

For what value of n is  ?

 

 

 

 

 

·       Recurrence relationships

 

A recurrence relation describes a sequence in which each

 term is a function of a previous term.

 

Example

 

 

 

Example

 

 

 

 

 

 

Example

 

 

An art dealer expects a painting worth £1 million to appreciate

in value by 5% per year.

a)              Find a recurrence relation for the value of the painting.

b)             Calculate the value of the painting after 5 years.

 

 

 

 

Example

 

 £50,000  is borrowed at 6.5% p.a, with a monthly repayment

of £ 322.50.

 

a)              How much is owed on the loan after 5 years ?

b)             How long does it take to pay off the loan ?

 

 

 

 

Carrying on the calculations

 

Year	Amount Owed £	Year	Amount Owed £
0	50000
1	49380	16	33412.51
2	48719.7	17	31714.33
3	48016.48	18	29905.76
4	47267.55	19	27979.63
5	46469.94	20	25928.31
6	45620.49	21	23743.65
7	44715.82	22	21416.99
8	43752.35	23	18939.09
9	42726.25	24	16300.13
10	41633.46	25	13489.64
11	40469.63	26	10496.47
12	39230.16	27	7308.736
13	37910.12	28	3913.804
14	36504.28	29	298.2012
15	35007.06	30	-3552.42

 

It takes 30 years to pay back the money.