    #### 1.   Work out the 11th term of the sequence 6, 9, 14, 21, 30, ...

 (a) Work out the difference between each term
 N 1 2 3 4 5 Nth term 6 9 14 21 30 1st differ. +3 +5 +7 +9 2nd differ. +2 +2 +2

 (b) Work out the formula
 As the 2nd difference is the same the sequence is a quadratic, try n2
 N 1 2 3 4 5 N2 1 4 9 16 25 differ. +5 +5 +5 +5 +5 Nth term 6 9 14 21 30 So the nth term = n2 + 5
 (c) Work out the 11th term:

#### 2.   Work out the 15th term of the sequence −3, 0, 5, 12, 21, ...

 (a) Work out the difference between each term
 N 1 2 3 4 5 Nth term −3 0 5 12 21 1st differ. +3 +5 +7 +9 2nd differ. +2 +2 +2

 (b) Work out the formula
 As the 2nd difference is the same the sequence is a quadratic, try n2
 N 1 2 3 4 5 N2 1 4 9 16 25 differ. −4 −4 −4 −4 −4 Nth term −3 0 5 12 21 So the nth term = n2 − 4
 (c) Work out the 15th term:

#### 3.   Work out the 17th term of the sequence −5, 1, 11, 25, 43, ...

 (a) Work out the difference between each term
 N 1 2 3 4 5 Nth term −5 1 11 25 43 1st differ. +6 +10 +14 +18 2nd differ. +4 +4 +4

 (b) Work out the formula
 As the 2nd difference is the same the sequence is a quadratic, try 2n2
 N 1 2 3 4 5 2n2 2 8 18 32 50 differ. −7 −7 −7 −7 −7 Nth term −5 1 11 25 43 So the nth term = 2n2 − 7
 (c) Work out the 17th term:

#### 4.   Work out the 9th term of the sequence 14, 20, 30, 44, 62, ...

 (a) Work out the difference between each term
 N 1 2 3 4 5 Nth term 14 20 30 44 62 1st differ. +6 +10 +14 +18 2nd differ. +4 +4 +4

 (b) Work out the formula
 As the 2nd difference is the same the sequence is a quadratic, try 2n2
 N 1 2 3 4 5 2n2 2 8 18 32 50 differ. +12 +12 +12 +12 +12 Nth term 14 20 30 44 62 So the nth term = 2n2 + 12
 (c) Work out the 9th term:

#### 5.   Work out the 20th term of the sequence 10, 19, 34, 55, 82, ...

 (a) Work out the difference between each term
 N 1 2 3 4 5 Nth term 10 19 34 55 82 1st differ. +9 +15 +21 +27 2nd differ. +6 +6 +6

 (b) Work out the formula
 As the 2nd difference is the same the sequence is a quadratic, try 3n2
 N 1 2 3 4 5 3n2 3 12 27 48 75 differ. +7 +7 +7 +7 +7 Nth term 10 19 34 55 82 So the nth term = 3n2 + 7
 (c) Work out the 20th term:

#### 6.   Work out the 19th term of the sequence −9, 0, 15, 36, 63, ...

 (a) Work out the difference between each term
 N 1 2 3 4 5 Nth term −9 0 15 36 63 1st differ. +9 +15 +21 +27 2nd differ. +6 +6 +6

 (b) Work out the formula
 As the 2nd difference is the same the sequence is a quadratic, try 3n2
 N 1 2 3 4 5 3n2 3 12 27 48 75 differ. −12 −12 −12 −12 −12 Nth term −9 0 15 36 63 So the nth term = 3n2 − 12
 (c) Work out the 19th term:

#### 7.   Work out the 21st term of the sequence 14, 23, 38, 59, 86, ...

 (a) Work out the difference between each term
 N 1 2 3 4 5 Nth term 14 23 38 59 86 1st differ. +9 +15 +21 +27 2nd differ. +6 +6 +6

 (b) Work out the formula
 As the 2nd difference is the same the sequence is a quadratic, try 3n2
 N 1 2 3 4 5 3n2 3 12 27 48 75 differ. +11 +11 +11 +11 +11 Nth term 14 23 38 59 86 So the nth term = 3n2 + 11
 (c) Work out the 21st term: back to:   