    #### 1.   Work out the 55th term in the sequence 7, 14, 21, 28, 35

 N 1 2 3 4 5 Nth term 7 14 21 28 35 Difference +7 +7 +7 +7

The difference between each term is 7, so the formula involves the 7 times table.

 (a) Work out the formula Try the formula 7n for the 1st term. 7 x 1 = 7. The 1st term is equal to 7 So nth term = 7n.
 (b) Work out the 55th term: 55th term = 7 x 55 = 385

#### 2.   Work out the 20th term in the sequence 11, 18, 25, 32, 39

 N 1 2 3 4 5 Nth term 11 18 25 32 39 Difference +7 +7 +7 +7

The difference between each term is 7, so the formula involves the 7 times table.

 (a) Work out the formula Try the formula 7n for the 1st term. 7 x 1 = 7. But the 1st term is equal to 11. So add 4. Try the formula 7n + 4 for the 1st term: 1st term = 7 × 1 + 4 = 7 + 4 = 11 So nth term = 7n + 4
 (b) Work out the 20th term: 20th term = 7 × 20 + 4 = 140 + 4 = 144

#### 3.   The 6th, 7th and 8th terms in a sequence are 37, 44 and 51. Work out the 1st and 17th terms

 N 1 ~ 6 7 8 Nth term ~ 37 44 51 Difference +7 +7

 (a) Work out the first term Here the first 5 terms are missing. 1st term = 6th term − total of the first five terms 1st term = 37 − (7 × 5) = 37 − 35 = 2
 (b) Work out the formula Try the formula 7n for the 1st term. 7 x 1 = 7. But the 1st term is equal to 2. So subtract 5. Try the formula 7n − 5 for the 1st term: 1st term = 7 × 1 − 5 = 7 − 5 = 2 So nth term = 7n − 5
 (c) Work out the 17th term: 17th term = 7 × 17 − 5 = 119 − 5 = 114

#### 4.   Work out the 29th term in the sequence 14, 28, 42, 56, 70

 N 1 2 3 4 5 Nth term 14 28 42 56 70 Difference +14 +14 +14 +14

The difference between each term is 14, so the formula involves the 14 times table.

 (a) Work out the formula Try the formula 14n for the 1st term. 14 x 1 = 14. The 1st term is equal to 14 So nth term = 14n.
 (b) Work out the 29th term: 29th term = 14 x 29 = 406

#### 5.   Work out the 17th term in the sequence 5, 19, 33, 47, 61

 N 1 2 3 4 5 Nth term 5 19 33 47 61 Difference +14 +14 +14 +14

The difference between each term is 14, so the formula involves the 14

 (a) Work out the formula Try the formula 14n for the 1st term. 14 x 1 = 14. But the 1st term is equal to 5. So subtract 9. Try the formula 14n − 9 for the 1st term: 1st term = 14 × 1 − 9 = 14 − 9 = 5 So nth term = 14n − 9
 (b) Work out the 17th term: 17th term = 14 × 17 − 9 = 238 − 9 = 229

#### 6.   The 7th, 8th and 9th terms in a sequence are 110, 124 and 138. Work out the 1st and 15th term

 N 1 ~ 7 8 9 Nth term ~ 110 124 138 Difference +14 +14

 (a) Work out the first term Here the first 6 terms are missing. 1st term = 7th term − total of the first six terms 1st term = 110 − (6 × 14) = 110 − 84 = 26
 (b) Work out the formula Try the formula 14n for the 1st term. 14 x 1 = 14. But the 1st term is equal to 26. So add 12. Try the formula 14n + 12 for the 1st term: 1st term = 14 × 1 + 12 = 14 + 12 = 26 So nth term = 14n + 12
 (c) Work out the 15th term: 15th term = 14 × 15 + 12 = 210 + 12 = 222

#### 7.   The 8th, 9th and 10th terms in a sequence are 81, 92 and 103. Work out the 1st and 24th term

 N 1 ~ 8 9 10 Nth term ~ 81 92 103 Difference +11 +11

 (a) Work out the first term Here the first 7 terms are missing. 1st term = 8th term − total of the first seven terms 1st term = 81 − (7 × 11) = 81 − 77 = 4
 (b) Work out the formula Try the formula 11n for the 1st term. 11 x 1 = 11. But the 1st term is equal to 4. So subtract 7. Try the formula 11n − 7 for the 1st term: 1st term = 11 × 1 − 7 = 11 − 7 = 4 So nth term = 11n − 7
 (c) Work out the 24th term: 24th term = 11 × 24 − 7 = 264 − 7 = 257 back to:   