a gardener is making a triangle planting with 35 plants in row ,31 in the second row ,27 in the third row and so on . if the pattern is considered how many plants will be there in the last row?
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The nth row has 35-4(n-1) = 39-4n plants.
So, what is the largest multiple of 4 less than 39? Subtract that from 39.
Or, just divide 39 by 4. The remainder is how many plants are in the last row. It is the row that is too short to subtract 4 from it again.
To find out how many plants will be in the last row, we need to analyze the pattern in the number of plants in each row.
From the given information, we can observe that the number of plants in each row is decreasing by 4 each time.
So, we can write the pattern as follows:
Row 1: 35 plants
Row 2: 35 - 4 = 31 plants
Row 3: 31 - 4 = 27 plants
Row 4: 27 - 4 = 23 plants
We can continue this pattern until we find the last row.
Row 5: 23 - 4 = 19 plants
Row 6: 19 - 4 = 15 plants
Row 7: 15 - 4 = 11 plants
Row 8: 11 - 4 = 7 plants
Row 9: 7 - 4 = 3 plants
Since there are only 3 plants in the 9th row, we can conclude that the 9th row is the last row.
Therefore, there will be 3 plants in the last row.
To find the number of plants in the last row, you can notice a pattern in the given sequence.
The first row has 35 plants, the second row has 31 plants, and so on. We can see that each row has 4 fewer plants than the previous row.
Therefore, you can find the number of plants in the last row by subtracting multiples of 4 from the number of plants in the first row until you reach the last row.
Starting with the first row having 35 plants, subtract 4 to find the second row: 35 - 4 = 31 plants.
Then subtract 4 again to find the third row: 31 - 4 = 27 plants.
Continue subtracting 4 until you reach the last row.
The number of times you subtract 4 depends on how many rows there are.
To find the number of rows, you can see that each row decreases by 4 plants. So you can find the number of rows by dividing the difference between the first and last row by 4:
35 - x = 4 * (n - 1)
Where x is the number of plants in the last row and n is the number of rows.
In this case, we start with 35 plants and want to find the number of rows until we reach the last row, so we solve for n:
35 - x = 4 * (n - 1)
35 - x = 4n - 4
x - 4n = -4 + 35
x = 4n + 31
We want to find the last row, so we can let n = 1 (since the first row is the last row). Plugging n = 1 into the equation:
x = 4(1) + 31
x = 4 + 31
x = 35
Therefore, the last row will have 35 plants.