To solve this problem, we need to find the pattern in the number of elements in each row and the first number in each row.
From observation, we can see that the number of elements in each row increases by 2. In row 1, there is 1 element, in row 2 there are 3 elements, in row 3 there are 5 elements, and so on.
For the first number in each row, we can observe that it follows a pattern as well. Row 1 starts with 1, row 2 starts with 3, row 3 starts with 9, and so on. The first number in each row can be calculated using the formula:
First number in row n = (n-1)^2 + 1
To find the middle number in the 60th row, we need to determine the total number of elements in rows 1 to 60.
Sum of first n odd numbers = n^2
Thus, the number of elements in the 60th row is 60^2 = 3600.
Now, let's find the first number in the 60th row:
First number in row 60 = (60-1)^2 + 1
= 59^2 + 1
= 3481 + 1
= 3482
Since there are 3600 elements in the row, and the middle element is the 1801st element (3600/2 + 1), we'll find the middle number.
Middle number in row 60 = First number in row 60 + 1800
= 3482 + 1800
= 5282
Therefore, the middle number in the 60th row is 5282.
the uneven natural numbers are written in a pattern as shown
row 1: 1
row 2: 3 5 7
row 3: 9 11 13 15 17
row 4: 19 21 23 25 27 29 31
what is the middle number in the 60th row
1 answer