Homework 5 on Sequences and Business Arithmetic Part 2    
                       
        Your Score:          
                       
Q1) The first five terms of an arithmetic sequence are:    
  1 2 3 4 5            
  234 228 222 216 210            
                       
  What is the nth term formula? n  +    
                       
  After how many terms will the sequence be less than -500 ?      
                       
Q2) Term  7 of an arithmetic sequence is: 39          
  Term  20 of the same sequence is:   130          
                       
  Find the first term and the common difference:              
                       
    a = d =            
                       
Q3) An arithmetic progression has a first term of  -30            
  and a common difference of 3              
  Find the sum of the first  500 terms.            
                       
  Sum =                  
                       
Q4) Term 21 of an Arithmetic Progression is 122          
  The sum of the first 39 terms of the same progression is 4512.3        
  Find the first term and the common difference.              
                       
  a = d =              
                       
Q5) Find term 12 of the following sequence:      
                       
  0.2 0.5 1.25 3.125 7.8125 . . . . .         
                       
                       
Q6) Term 6 of a geometric sequence is -2048            
  Term  3 the same sequence is -32            
                       
  Find the first term and the value of the ratio.      
                       
    a =                
    r1 =                 
                       
  List the first five terms of the sequence below:              
                       
             
                       
                       
Q7) If possible, find the sum to infinity of the following series.            
  If the series is divergent, enter "d".                
                       
  a) 3 1.2 0.48 0.192 0.0768   Sinf =    
                       
                       
  b) 3 4.2 5.88 8.232 11.5248   Sinf =    
                       
                       
  c) 3 -1.2 0.48 -0.192 0.0768   Sinf =    
                       
                       
                       
Q8) Term 4 of a geometric sequence is   13.5          
  Term  2 the same sequence is   24          
                       
  Find the sum to infinity of this series:      
                       
    a =                
    r =                
    S =                
                       
                       
Q9) You're saving up for a boat which costs £240,000            
  You deposit £23,400 at the start of each year into an account.          
  The account pays compound interest at 3.100% paid at the end of each year.      
                       
  a) What is the value of the investment at the end of year    6      
                       
  b) How long will it take to save up for the boat?       years    
                       
                       
Challenge Question                
                       
Q10) The mortgage on a house is  £468,000              
  The bank charges 0.210% on the outstanding debt each month.          
  The monthly repayments are £2,600.00              
                       
  How many month will it take to repay the loan?   months        
            years