Sequences

Formula for the nth term of a sequence

Example

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.

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

• How much is owed on the loan after 5 years ?
• How long does it take to pay off the loan ?

 

Carrying on the calculations

It takes 30 years to pay back the money.