EXERCISE 26D
1 Use the method of differences to find the general termunof:
a 1 , 5 , 9 , 13 , 17 , 21 , ...... b 17 , 14 , 11 , 8 , 5 , 2 , ......
c 2 , 6 , 12 , 20 , 30 , 42 , ...... d 0 , 6 , 14 , 24 , 36 , 50 , ......
e 6 , 13 , 32 , 69 , 130 , 221 , 348 , ...... f 2 , 7 , 18 , 38 , 70 , 117 , 182 , ......
2 Consider the sequence: 2 , 12 , 30 , 56 , 90 , 132 , ......
a Use the difference method to find the general term un.
b Suggest an alternative formula forunby considering u 1 =1£ 2 , u 2 =::::::£::::::,
u 3 =::::::£::::::, and so on.3 Consider the dot pattern:a Find un for n=1, 2 , 3 , 4 , 5 , 6 and 7.
b Find a formula for the general term un.
c How many dots are needed to make up the 30 th figure in the pattern?4 These diagrams represent the hand-shakes between two people (A and B), three people (A, B and C),
four people (A, B, C and D), and so on.a
b When you are sure that you have counted them correctly, find the formula for the general term un
of the sequence 1 , 3 , 6 , 10 , ......
c 179 delegates attend a conference. If every person shakes hands with every other person, how
many hand-shakes take place?5 Consider the sequenceunwhere: u 1 =1£ 3
u 2 =1£3+2£ 5
u 3 =1£3+2£5+3£ 7
u 4 =1£3+2£5+3£7+4£ 9 and so on.
a Find the values of u 1 ,u 2 ,u 3 ,u 4 ,u 5 ,u 6 andu 7.
b Use the difference method to find a formula for un.
c Hence, find the value of u 50.6 Consider theOpening Problemon page 533.
Notice that: u 1 =1^2
u 2 =1^2 +2^2
u 3 =1^2 +2^2 +3^2
u 4 =1^2 +2^2 +3^2 +4^2
a Find un for n=1, 2 , 3 , 4 , 5 , 6 and 7.
b Use the difference method to find a formula for un.
c How many squares are contained in a 100 by 100 square?, , , .....ABAB CA DB CA
B CDE(1) (3) (6) (10)
Draw diagrams showing hand-shakes for ,67 8and people.Sequences (Chapter 26) 543IGCSE01
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100 100
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100 100
Y:\HAESE\IGCSE01\IG01_26\543IGCSE01_26.CDR Thursday, 30 October 2008 1:55:27 PM PETER