Number Patterns

1. 1, 3, 5, 7, ....., ..... ..

1, 3, 5, 7, 10, 13..

1, 4, 7, 10, 13..

1, 3, 5, 7, 9, 11.

1, 3, 5, 7, 9, 10..

The pattern in the sequence is incrementing by 2 starting from 1 to form odd numbers, so the next numbers should be 9, 11 to maintain this pattern.

Explanation

The pattern in the sequence is incrementing by 2 starting from 1 to form odd numbers, so the next numbers should be 9, 11 to maintain this pattern.

2. 1, 2, 4, 7, ..... , ..... ..

1, 2, 4, 7, 13, 20

1, 2, 4, 7, 11, 16 .

1, 2, 4, 8, 14, 22

1, 2, 4, 6, 9, 14

The series is based on adding successive prime numbers to the previous number. In the correct answer, the differences between the numbers are 1, 2, 3, 4, 5, hence the missing numbers are prime numbers (11, 13, 17) added to the last number in the sequence.

Explanation

The series is based on adding successive prime numbers to the previous number. In the correct answer, the differences between the numbers are 1, 2, 3, 4, 5, hence the missing numbers are prime numbers (11, 13, 17) added to the last number in the sequence.

3. 1, 4, 9, 16, ..... , ..... ..

1, 4, 9, 16, 25 , 36 .

1, 4, 7, 11, 16 ...

1, 2, 3, 5, 8 ...

1, 4, 9, 16, 20, 25 ...

The sequence provided is the square of natural numbers: 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36. Option 1 does not follow the pattern of square numbers. Option 2 shows a sequence that is not formed by squaring the natural numbers. Option 3 shows a Fibonacci sequence, which does not fit the given pattern.

Explanation

The sequence provided is the square of natural numbers: 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36. Option 1 does not follow the pattern of square numbers. Option 2 shows a sequence that is not formed by squaring the natural numbers. Option 3 shows a Fibonacci sequence, which does not fit the given pattern.

4. 1, 4, 7, 10, ..... , ..... ..

1, 4, 7, 10, 13, 16 .

2, 5, 8, 11, 14

1, 3, 6, 9, 12

1, 4, 8, 10, 14

The pattern in the question is an arithmetic sequence with a common difference of 3. Each term is obtained by adding 3 to the previous term. The correct sequence follows this pattern, with each term increasing by 3.

Explanation

The pattern in the question is an arithmetic sequence with a common difference of 3. Each term is obtained by adding 3 to the previous term. The correct sequence follows this pattern, with each term increasing by 3.

5. Write down the number of triangles in the fourth diagram: 1, 5, 13, ......

15

8

18

1, 5, 13, 21.

The pattern in the numbers represents the increasing number of triangles in each diagram. The correct sequence is achieved by adding 4 to the previous number in the series. Therefore, the next number after 13 would be 13 + 4 = 17, then 17 + 4 = 21.

Explanation

The pattern in the numbers represents the increasing number of triangles in each diagram. The correct sequence is achieved by adding 4 to the previous number in the series. Therefore, the next number after 13 would be 13 + 4 = 17, then 17 + 4 = 21.