Question 1: Write the next three numbers in each of the following sequences. Say whether each sequence is a constant difference or constant ratio sequence or neither.

Here are the solutions to the sequences: Question 1: Write the next three numbers in each of the following sequences. Say whether each sequence is a constant difference or constant ratio sequence or neither. a) 3, 6, 9, 12, 15, ... Step 1: Find the difference between consecutive terms. 6-3=3 9-6=3 12-9=3 15-12=3 The difference is constant (3). This is a constant difference sequence. Step 2: Add the constant difference to find the next three terms. 15+3=18 18+3=21 21+3=24 The next three numbers are 18, 21, 24. The sequence is a constant difference sequence. 18, 21, 24; Constant difference b) 2, 4, 8, 16, ... Step 1: Find the ratio between consecutive terms. (4)/(2)=2 (8)/(4)=2 (16)/(8)=2 The ratio is constant (2). This is a constant ratio sequence. Step 2: Multiply by the constant ratio to find the next three terms. 16 × 2=32 32 × 2=64 64 × 2=128 The next three numbers are 32, 64, 128. The sequence is a constant ratio sequence. 32, 64, 128; Constant ratio c) 7, 11, 15, 19, 23, ... Step 1: Find the difference between consecutive terms. 11-7=4 15-11=4 19-15=4 23-19=4 The difference is constant (4). This is a constant difference sequence. Step 2: Add the constant difference to find the next three terms. 23+4=27 27+4=31 31+4=35 The next three numbers are 27, 31, 35. The sequence is a constant difference sequence. 27, 31, 35; Constant difference d) 1, 4, 9, 16, ... Step 1: Check for constant difference. 4-1=3 9-4=5 16-9=7 The differences are not constant. Step 2: Check for constant ratio. (4)/(1)=4 (9)/(4)=2.25 The ratios are not constant. Step 3: Observe the pattern. The terms are squares of consecutive integers: 1^2, 2^2, 3^2, 4^2. Step 4: Find the next three terms. 5^2=25 6^2=36 7^2=49 The next three numbers are 25, 36, 49. The sequence is neither a constant difference nor a constant ratio sequence. 25, 36, 49; Neither Question 2: Describe the pattern in each of the following sequences. State whether it is a constant difference or constant ratio sequence or neither. Then fill in the missing numbers. a) 18, 36, 54, 72, [ ], [ ], [ ] Step 1: Find the difference between consecutive terms. 36-18=18 54-36=18 72-54=18 The difference is constant (18). This is a constant difference sequence. Step 2: Add the constant difference to find the missing terms. 72+18=90 90+18=108 108+18=126 The pattern is adding 18 to the previous term. The sequence is a constant difference sequence. The missing numbers are 90, 108, 126. Constant difference; 90, 108, 126 b) 3, 9, 27, [ ], [ ], [ ] Step 1: Find the ratio between consecutive terms. (9)/(3)=3 (27)/(9)=3 The ratio is constant (3). This is a constant ratio sequence. Step 2: Multiply by the constant ratio to find the missing terms. 27 × 3=81 81 × 3=243 243 × 3=729 The pattern is multiplying the previous term by 3. The sequence is a constant ratio sequence. The missing numbers are 81, 243, 729. Constant ratio; 81, 243, 729 *c) 1.25, 2.5, 3.75, 5.0, [ ], [ ], [