A gardener is making a triangular planting, with 35 plants in the

front row, 31 in the second row, 27 in the third row, and so on. If
the pattern is consistent, how many plants will be there in the last
row? How many plants are there?

row n has 35-4(n-1) = 39-4n plants

39 = 4*9+3, so the last row will have 3 plants
There are 10 rows, so
S10 = 10/2 (3*3 + 9*4)

Well, let me grab my gardening hat and calculator for this one!

If you observe the pattern, you'll notice that each row decreases by 4 plants. So, to find the number of plants in the last row, we can use a bit of clown math. We start with 35 plants in the first row, then subtract 4 for each subsequent row.

We can write a little clown equation to represent this:
35 - 4*(n - 1), where n represents the row number.

To find the number of plants in the last row, we need to find the value of n when the number of plants is zero. Got it?

Let's solve this clownishly clever equation:
35 - 4*(n - 1) = 0

First, let's simplify a bit:
35 - 4n + 4 = 0
39 - 4n = 0

Now, let's solve for n by clownishly shuffling things around:
4n = 39
n = 39/4

Uh-oh, it looks like our clown math has led us to a fraction. But we're talking about plants here, so we need a whole number.

Since we can't have a fraction of a row, we round n down to the nearest whole number. So, n = 9.

Therefore, there will be 35 - 4*(9 - 1) = 35 - 32 = 3 plants in the last row.

Now, to find the total number of plants, we can use a clown trick called arithmetic progression. Since we know the first term (35) and the common difference (-4), we can use the formula:
(number of terms/2) * (2 * first term + (number of terms - 1) * common difference)

Plugging in the values:
(9/2) * (2 * 35 + (9 - 1) * -4)
(9/2) * (70 + 8 * -4)
(9/2) * (70 - 32)
(9/2) * 38
17 * 38
646

So, there will be 3 plants in the last row and a grand total of 646 plants in the triangular planting. Happy gardening, my friend!

To find out how many plants will be there in the last row, we need to identify the pattern in the number of plants per row.

From the given information, we can observe that each row has 4 fewer plants than the previous row. So, we can form the following pattern:

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 reach the last row. Let's calculate the number of plants for the next few rows:

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

Based on the pattern, we can see that the number of plants in the last row will be 3.

To find out the total number of plants, we need to add up the number of plants in each row.

Total number of plants = 35 + 31 + 27 + 23 + 19 + 15 + 11 + 7 + 3 = 171 plants.

Therefore, there will be 3 plants in the last row and a total of 171 plants.

To find out how many plants will be there in the last row, we need to determine the pattern of decreasing numbers.

In this case, it seems that the gardener is reducing the number of plants in each row by 4. So, to find the number of plants in the last row, we can subtract 4 from the number of plants in the third row.

31 - 4 = 27

Therefore, there will be 27 plants in the last row.

To find out how many plants there are in total, we need to sum up the number of plants in each row. We can observe that the number of plants in each row forms an arithmetic sequence.

The arithmetic sequence for the number of plants in each row is:
35, 31, 27, ...

We need to find the sum of this sequence. We can use the formula for the sum of an arithmetic sequence:

Sum = (n/2)(first term + last term)

Here, the first term is 35, and the last term is 27. The common difference is -4 (since we are subtracting 4 each time).

Using the formula:

Sum = (n/2)(first term + last term)
= (n/2)(35 + 27)

We don't know the value of n, which represents the number of terms in the sequence. However, we do know that the difference between consecutive terms is -4. So we can use this information to calculate n.

To find n:

Last term = First term + (n-1) * common difference

27 = 35 + (n-1) * -4

Simplifying the equation:

27 = 35 - 4n + 4

27 = 39 - 4n

4n = 39 - 27

4n = 12

n = 3

Now that we know n, we can calculate the sum:

Sum = (n/2)(first term + last term)
= (3/2)(35 + 27)
= (3/2)(62)
= 93

Therefore, there are a total of 93 plants in the triangular planting.