Answer :
Let's identify and extend the patterns in each sequence given.
a) The sequence is: 4, 8, 16, ____, ____, ____.
Notice that each number is doubled to get the next number:
- Start with 4: [tex]4 \times 2 = 8[/tex]
- Next: [tex]8 \times 2 = 16[/tex]
- Following this pattern, we get:
- [tex]16 \times 2 = 32[/tex]
- [tex]32 \times 2 = 64[/tex]
- [tex]64 \times 2 = 128[/tex]
So the next numbers are 32, 64, and 128.
b) The sequence is: 5, 10, 20, ____, ____, ____.
Here, too, each number is doubled:
- Start with 5: [tex]5 \times 2 = 10[/tex]
- Next: [tex]10 \times 2 = 20[/tex]
- Continue:
- [tex]20 \times 2 = 40[/tex]
- [tex]40 \times 2 = 80[/tex]
- [tex]80 \times 2 = 160[/tex]
The next numbers are 40, 80, and 160.
c) The sequence is: 1600, 800, 400, ____, ____, ____.
This sequence halves each time:
- Start with 1600: [tex]\frac{1600}{2} = 800[/tex]
- Next: [tex]\frac{800}{2} = 400[/tex]
- Continue:
- [tex]\frac{400}{2} = 200[/tex]
- [tex]\frac{200}{2} = 100[/tex]
- [tex]\frac{100}{2} = 50[/tex]
The next numbers are 200, 100, and 50.
d) The sequence is: 1, 3, 9, 27, ____, ____, ____.
Observe the pattern of multiplying by 3:
- Start with 1: [tex]1 \times 3 = 3[/tex]
- Next: [tex]3 \times 3 = 9[/tex]
- Continue:
- [tex]9 \times 3 = 27[/tex]
- [tex]27 \times 3 = 81[/tex]
- [tex]81 \times 3 = 243[/tex]
The next numbers are 81, 243, and 729.
e) The sequence is: 96, 48, 24, ____, ____, ____.
This pattern involves halving:
- Start with 96: [tex]\frac{96}{2} = 48[/tex]
- Next: [tex]\frac{48}{2} = 24[/tex]
- Continue:
- [tex]\frac{24}{2} = 12[/tex]
- [tex]\frac{12}{2} = 6[/tex]
- [tex]\frac{6}{2} = 3[/tex]
The next numbers are 12, 6, and 3.
f) The sequence is: 3125, 625, 125, ____, ____, ____.
Each term, when divided by 5, produces the next:
- Start with 3125: [tex]\frac{3125}{5} = 625[/tex]
- Next: [tex]\frac{625}{5} = 125[/tex]
- Continue:
- [tex]\frac{125}{5} = 25[/tex]
- [tex]\frac{25}{5} = 5[/tex]
- [tex]\frac{5}{5} = 1[/tex]
The next numbers are 25, 5, and 1.
