Answer :
Final Answer:
The pattern for the numbers in each diamond is as follows:
Diamond 1:
1
2 3
4 5 6
7 8 9 10
Diamond 2:
1
3 5
7 9 11
13 15 17 19
Diamond 3:
2
4 8
16 32 64
128 256 512 1024
Diamond 4:
1
4 9
16 25 36
49 64 81 100
Explanation:
In each diamond, the numbers follow a specific pattern:
Diamond 1:
- Each row contains consecutive positive integers.
- The first row starts with 1, the second row starts with the next consecutive number after the last number in the previous row, and so on.
Diamond 2:
- Each row contains consecutive odd numbers.
- The first row starts with 1, the second row starts with the next odd number after the last number in the previous row, and so on.
Diamond 3:
- Each row contains powers of 2.
- The first row starts with 2, and each subsequent row multiplies the last number in the previous row by 2.
Diamond 4:
- Each row contains perfect squares.
- The first row starts with 1, the second row starts with the square of the row number, and each subsequent row adds consecutive odd numbers to the last number in the previous row.
Patterns in number sequences and series. This concept is fundamental in mathematics and has wide applications in various fields including algebra, calculus, and number theory. Understanding patterns helps in making predictions, solving equations, and analyzing complex mathematical structures.
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