Cambridge International Mathematics

7 Consider the pattern:

a Supposeunis the number of squares contained in thenth figure, sou 1 =2andu 2 =6+2=8.

Find the values ofu 3 ,u 4 ,u 5 andu 6.

b Find a formula for un.

c How many squares are contained in the 15 th figure?

Review set 26A

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1 Write down a rule for the sequence and find its next two terms:

a 6 , 10 , 14 , 18 , 22 , ...... b 810 , 270 , 90 , 30 , ......

2

ab

3 Find the first four terms of the sequence withnth term:

a un=6n¡ 1 b un=n^2 +5n¡ 2

4aFind a formula for the general termunof the sequence: 4 , 8 , 12 , 16 , ......

b Hencefind un for:

i 1 , 5 , 9 , 13 , ...... ii^13 ,^17 , 111 , 151 , ......

c Find the 20 th term for each of the sequences inb.

5 List the first four terms of the geometric sequence defined by:

a un=27£(^23 )n b un=5£(¡2)n¡^1

6 Find un for the sequence:

a 3 , 12 , 48 , 192 , ...... b 88 ,¡ 44 , 22 ,¡ 11 , ......

7 Use the method of differences to find the general term un of:

a 5 , 12 , 19 , 26 , 33 , ...... b ¡ 1 , 6 , 15 , 26 , 39 , 54 , ......

8 Consider the figures:

Suppose un is the number of triangles in thenth figure, so u 1 =1and u 2 =5( 4 small

triangles and 1 large triangle).

a Find un for n=3, 4 , 5.

b Use the method of differences to find a formula for un.

c How many triangles are in the 50 th figure?

,

,

,

,.....

, , , .....

, , , .....

, , , .....

Draw the next matchstick figures in the pattern and write down the number of matchsticks

used as a number sequence:

two

544 Sequences (Chapter 26)

IGCSE01

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Y:\HAESE\IGCSE01\IG01_26\544IGCSE01_26.CDR Monday, 27 October 2008 2:36:31 PM PETER