{1} {2,3} {4,5,6} {7,8,9,10} {11,12,13,14,15} 1 is the first element and 2,3 is the second what is the first number in the 100 element of the sequence
To find the first number in the 100th element of the given sequence, we need to determine the pattern in the sequence and then apply it to calculate the desired value.
Looking at the provided sequence, we can observe the following pattern:
- The first element is {1}.
- The second element is {2,3}.
- The third element is {4,5,6}.
- The fourth element is {7,8,9,10}.
- The fifth element is {11,12,13,14,15}.
- The sixth element is {16,17,18,19,20,21}, and so on.
From this pattern, we can derive the formula to calculate the number of elements in the nth row:
number of elements = n + (n-1)
Now, let's consider the given sequence and determine the row number that contains the 100th element. By calculating the cumulative count of elements in each row, we can find the row number:
- Row 1 has 1 element.
- Row 2 has 2 + 1 = 3 elements.
- Row 3 has 3 + 2 = 5 elements.
- Row 4 has 4 + 3 = 7 elements.
- Row 5 has 5 + 4 = 9 elements.
- Row 6 has 6 + 5 = 11 elements.
By comparing the cumulative count, we see that Row 6 contains the 100th element. So, we need to find the first number in the 6th row of the sequence.
To calculate the first number in the 6th row, we need to determine the number of elements in the previous rows:
- Row 1: 1 element.
- Row 2: 3 elements.
- Row 3: 5 elements.
- Row 4: 7 elements.
- Row 5: 9 elements.
By summing the number of elements in each row, we get 1 + 3 + 5 + 7 + 9 = 25.
Since the 6th row starts at 25, and each row increases by 1, the first number in the 6th row would be 25.
Therefore, the first number in the 100th element of the sequence is 25.