8 Use the method of differences to find the general term un of:
a 43 , 34 , 25 , 16 , 7 , ...... b 4 , 12 , 22 , 34 , 48 , ......
9 Consider the sequence of figures:Suppose un is the number of matchsticks required to make thenth figure, so u 1 =4and
u 2 =12.
a Find un for n=3, 4 , 5 , 6.
b Use the method of differences to find a formula for un.
c How many matches are in the 10 th figure?10 Consider the sequence of figures:, , , .....
, , , .....
Suppose un is the number of rectangles present in thenth figure, so, u 1 =0, u 2 =1, and
u 3 =5.
a Show thatu 4 =15,u 5 =35, andu 6 =70.
b Show that neither a linear, quadratic or cubic model fit the data.
c Use technology to show that a quartic model fits the data. Give the quartic in the form
an^4 +bn^3 +cn^2 +dn+e, wherea,b,c,dande 2 Q, written in fractional form.546 Sequences (Chapter 26)IGCSE01
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Y:\HAESE\IGCSE01\IG01_26\546IGCSE01_26.CDR Wednesday, 12 November 2008 9:11:33 AM PETER