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Answer :
Let's analyze each sequence one by one and find the next three numbers in the sequence by identifying the pattern.
a. Sequence: 20; 40; 80; 160; ...
The pattern here is that each number is multiplied by 2 to get the next number.
- Next number after 160 is $160 \times 2 = 320$
- The following number is $320 \times 2 = 640$
- Then $640 \times 2 = 1280$
So, the next three numbers are 320; 640; 1280.
b. Sequence: 1; 2; 4; 8; ...
This sequence also involves multiplying each number by 2 to find the next one.
- Next number after 8 is $8 \times 2 = 16$
- Then $16 \times 2 = 32$
- Finally $32 \times 2 = 64$
So, the next three numbers are 16; 32; 64.
c. Sequence: 103; 84; 65; ...
Here, each term is obtained by subtracting 19 from the previous term.
- Next number after 65 is $65 - 19 = 46$
- Then $46 - 19 = 27$
- Finally $27 - 19 = 8$
So, the next three numbers are 46; 27; 8.
d. Sequence: 4; 12; 36; 108; ...
This sequence is generated by multiplying each number by 3.
- Next number after 108 is $108 \times 3 = 324$
- Then $324 \times 3 = 972$
- Finally $972 \times 3 = 2916$
So, the next three numbers are 324; 972; 2916.
e. Sequence: 1,000,000; 500,000; 250,000; ...
This sequence decreases by dividing each number by 2.
- Next number after 250,000 is $250,000 \div 2 = 125,000$
- Then $125,000 \div 2 = 62,500$
- Finally $62,500 \div 2 = 31,250$
So, the next three numbers are 125,000; 62,500; 31,250.
f. Sequence: 5; 4 \frac{3}{4}; 4 \frac{1}{2}; 4 \frac{1}{4}; ...
This sequence involves subtracting [tex]\frac{1}{4}[/tex] from each previous term.
- Next number after 4 [tex]\frac{1}{4}[/tex] is $4 \frac{1}{4} - \frac{1}{4} = 4$
- Then $4 - \frac{1}{4} = 3 \frac{3}{4}$
- Finally $3 \frac{3}{4} - \frac{1}{4} = 3 \frac{1}{2}$
So, the next three numbers are 4; 3 \frac{3}{4}; 3 \frac{1}{2}.
g. Sequence: 1,000; 875; 750; ...
Here, we subtract 125 from each previous term to find the next one.
- Next number after 750 is $750 - 125 = 625$
- Then $625 - 125 = 500$
- Finally $500 - 125 = 375$
So, the next three numbers are 625; 500; 375.
h. Sequence: 4; 16; 64; 256; ...
This sequence is generated by multiplying each number by 4.
- Next number after 256 is $256 \times 4 = 1024$
- Then $1024 \times 4 = 4096$
- Finally $4096 \times 4 = 16384$
So, the next three numbers are 1024; 4096; 16384.
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