continue a pattern:

1; 10;3; 30 __; __; __;
150; 140; 170; 160; __; __; __;
5; 25; 50; 10; __; __; __;
2; 5; 10; 3; __; __; __;
1; 300; 2; 600; __; __; __;

your question of

'continue a pattern' is much too vague.

for example in the first one it might appear that you start with odd numbers and follow it by 10 times that odd number.
so
1,10,3,30,5,50,...

or 10-1 = 9 = 3^2
30 - 3 = 27 = 3^3

then 86 - 5 = 3^4

so my pattern could have been

1,10,3,30,5,86,...

Do you see what I mean?

In what context was the question asked?
What are you studying to have these kind of questions?
What grade level is this??

Thanks. I'm in 5th grade. It was just math question to continue these and other simple pattern:

1; 10; 3; 30 __; __; __;
150; 140; 170; 160; __; __; __;
5; 25; 50; 10; __; __; __;
2; 5; 10; 3; __; __; __;
1; 300; 2; 600; __; __; __;

my answers
continue a pattern:
1; 10; 3; 30; 9; 90; 27
150; 140; 170; 160; 190; 180; 210;
5; 25; 50; 10; 50; 100; 20;
1; 300; 2; 600; 4; 1200; 8;
here no idea
2; 5; 10; 3; ?; ? ; ?

To continue the given pattern, let's analyze each sequence separately:

Sequence 1: 1; 10; 3; 30; __; __; __;

Looking at the pattern, it seems that each subsequent number alternates between multiplying by 10 and dividing by 10. Starting with 1, we get 1 * 10 = 10, then 10 ÷ 10 = 1, and 1 * 10 = 10. So, the missing numbers in the sequence would be 10, 1, 10.

Sequence 2: 150; 140; 170; 160; __; __; __;

In this sequence, each number alternates between subtracting 10 and adding 30. Starting with 150, we get 150 - 10 = 140, then 140 + 30 = 170, and 170 - 10 = 160. So, the missing numbers in the sequence would be 170, 160, 190.

Sequence 3: 5; 25; 50; 10; __; __; __;

In this sequence, each number alternates between multiplying by 5 and dividing by 5. Starting with 5, we get 5 * 5 = 25, then 25 ÷ 5 = 5, and 5 * 5 = 25. So, the missing numbers in the sequence would be 5, 25, 125.

Sequence 4: 2; 5; 10; 3; __; __; __;

In this sequence, each number alternates between multiplying by 2 and dividing by 2. Starting with 2, we get 2 * 2 = 4, then 4 ÷ 2 = 2, and 2 * 2 = 4. So, the missing numbers in the sequence would be 4, 2, 4.

Sequence 5: 1; 300; 2; 600; __; __; __;

In this sequence, it seems that each number is multiplied by a certain factor to get the next number. Starting with 1, we get 1 * 300 = 300, then 300 ÷ 150 = 2, and 2 * 600 = 1200. So, the missing numbers in the sequence would be 300, 2, 1200.

The completed sequences are:

1; 10; 3; 30; 10; 1; 10;

150; 140; 170; 160; 170; 160; 190;

5; 25; 50; 10; 5; 25; 125;

2; 5; 10; 3; 4; 2; 4;

1; 300; 2; 600; 300; 2; 1200.