2.2 Finding the nth term Grade 8

Identify whether the given sequence is linear or non-linear.

 $20,\ 30,\ 40,\ 50,\ 60,\ ...$  

• Linear Sequence

• Non-linear Sequence

Identify whether the given sequence is linear or non-linear.

 $0.5,\ 1,\ 1.5,\ 2,\ 2.5,\ \ ...$  

• Linear Sequence

• Non-linear Sequence

Identify whether the given sequence is linear or non-linear.

 $20,\ 18,\ 15,\ 11,\ 6,\ ...$  

• Linear Sequence

• Non-linear Sequence

Identify the first four terms:

first term: 8
term-to-term rule: subtract 5

•  $8,\ 13,\ 18,\ 23$  
  

•  $13,\ 18,\ 23,\ 28$  
  

•  $3,−2,−7,-12$  

•  $8,3,−2,−7$  

The tenth term of a linear sequence is 18. 

The term-to-term rule is "subtract 4". 

Work out the fourth term of the sequence.

• 42

• 52

• 62

• 72

Use the position-to-term rule to work out the first four terms.

 $term\ =\ position\ number+5$  

• 7, 12, 17, 23

• 5, 10, 15, 20

• 6, 7, 8, 9

• 4,  9, 14, 19

Use the position-to-term rule to work out the fifth term:

 $term\ =\ 4\ \times\ position\ number+1$  

• 25

• 21

• 18

• 15

Work out an expression for the  $nth$  term for each sequence. 

 $23,\ 35,\ 47,\ 59,\ ...$  

•  $12n+11$  
  

•  $12n+23$  
  

•  $n+12$  
  

•  $n+23$  
  

Work out an expression for the  $nth$  term for each sequence. 

 $-2,\ -7,\ -12,\ -17,\ ...$  

•  $-2n+5$  
  

•  $n-5$  
  

•  $5n-3$  
  

•  $−5n+3$ 
  

Work out an expression for the  $nth$  term for each sequence. 

 $4,\ 9,\ 14,\ 19,\ ...$  

•  $5n+1$  
  

•  $5n−1$  
  

•  $-5n−1$  
  

•  $-5n+1$