Everything Maths Grade 10

3.3 Chapter summary EMA32

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• The general term is expressed as thenthterm and is written asTn.


• We define the common differencedof a sequence as the difference between any two successive terms,
  whered=TnT(n1)


• We can work out a general formula for each number pattern and use it to determine any term in the
  pattern.

End of chapter Exercise 3 – 2:

1.Analyse the diagram and complete the table.

Figure number (nn) 1  1 2  2 3  3 4  4 nn

Number of horizontal matches

Number of vertical matches

Total number of matches

2.Given a list of numbers:7 ; 4 ; 1 ;2 ;5 ;: : :determine the common difference for the list (if there

is one).

3.For the pattern here:0,55;0,99;2,49;3,91;: : :calculate the common difference.

If the pattern is not linear, write “no common difference”. Otherwise, give your answer as a decimal.

4.Consider the list shown here:2 ; 7 ; 12 ; 17 ; 22 ; 27 ; 32 ; 37 ;: : :

IfT 5 =22 what is the value ofTn 3?

5.Write down the next three terms in each of the following linear sequences:

a) 10,2;29,2;48,2;: : : b) 50 r; 46r; 42r;: : :

6.Given a sequence which starts with the numbers:6 ; 11 ; 16 ; 21 ;: : :determine the values ofT 6 and

T 8.

7.Given a list which starts with the letters:A;B;C;D;: : :determine the values ofT 6 andT 10.

8.Find the sixth term in each of the following sequences:

a) 4 ; 13 ; 22 ; 31 ;: : : b)5 ; 2 ;1 ;4 ;: : : c) 7,4;9,7; 12 ;14,3;: : :

9.Find the general formula for the following sequences and then find T 10 , T 15 and T 30

a)  18 ; 22 ; 26 ; 30 ; 34 ;: : : b) 1 ; 6 ; 13 ; 20 ; 27 ;: : :

10.The general term is given for each sequence below. Calculate the missing terms (each missing term is

represented by: : :).

a) 10 ;: : :; 14 ;: : :; 18 Tn= 2n+ 8 b) 2 ; 2 ; 6 ;: : :; 14 Tn= 4 n+ 6

c) 8 ;: : :; 38 ;: : :; 68 Tn= 15n 7

68 3.3. Chapter summary