Cambridge International Mathematics

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EXERCISE 26A

1 Write down a rule to describe the sequence and hence find its nexttwoterms:

a 5 , 8 , 11 , 14 , 17 , ...... b 2 , 9 , 16 , 23 , 30 , ...... c 8 , 19 , 30 , 41 , 52 , ......

d 38 , 34 , 30 , 26 , 22 , ...... e 3 ,¡ 2 ,¡ 7 ,¡ 12 ,¡ 17 , ...... f^12 , 2 , 312 , 5 , 612 , ......

2 Write down a rule to describe the sequence and hence find its nexttwoterms:

a 3 , 6 , 12 , 24 , 48 , ...... b 1 , 2 , 4 , 8 , 16 , ...... c 2 , 10 , 50 , 250 , ......

d 36 , 18 , 9 , 412 , ...... e 162 , 54 , 18 , 6 , ...... f 405 , 135 , 45 , 15 , ......

3 Find the nexttwoterms of:

a 0 , 1 , 4 , 9 , 16 , ...... b 1 , 4 , 9 , 16 , 25 , ...... c 0 , 1 , 8 , 27 , 64 , ......

d^14 ,^19 , 161 , 251 , ...... e 1 , 2 , 4 , 7 , 11 , ...... f 2 , 6 , 12 , 20 , 30 , ......

4 Write down a rule to describe the sequences and hence find its nextthreeterms:

a 1 , 1 , 2 , 3 , 5 , 8 , ...... b 1 , 3 , 4 , 7 , 11 , ...... c 5 , 8 , 12 , 18 , 24 , 30 , ......

5 Draw the nexttwomatchstick figures in these sequences and write the number of matchsticks used as

a number sequence:

ab

cd

ef

6 Draw the nexttwofigures in these sequences and write the number of dots used as a number sequence:

ab

cd

An alternative way to describe a sequence is to write an algebraic rule or formula for itsnth termun.

For example: un=3n+2, un=n^2 +n, un=

1

n

Since these are general formulae for all terms of their sequences,unis often called thegeneral term.

B ALGEBRAIC RULES FOR SEQUENCES [2.12]

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Sequences (Chapter 26) 535

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Y:\HAESE\IGCSE01\IG01_26\535IGCSE01_26.CDR Monday, 27 October 2008 2:36:02 PM PETER