If Angel plants the same number of pepper plant in each of 5 rows, he will have none left over. If he plants one in the first row and them one more in each row that he did in the previous row, he will plant peppers in only 4 rows how many plants does he have?
1+2+3+4=10 plants
To determine how many plants Angel has, we can use the concept of arithmetic progression.
In the first scenario, Angel plants the same number of pepper plants in each of the 5 rows, resulting in none left over. This indicates that the number of plants Angel has is a multiple of 5.
In the second scenario, Angel plants one pepper plant in the first row and then one more in each subsequent row. This indicates that the number of plants follows an arithmetic progression, where each term is incremented by 1 compared to the previous term.
Since Angel plants peppers in only 4 rows in the second scenario, we can determine the total number of plants using the formula for the sum of an arithmetic progression:
Sum = (n/2) * (2a + (n-1)d),
where:
- n represents the number of terms (rows),
- a represents the first term (number of plants in the first row),
- d represents the common difference (increment in the number of plants from one row to the next).
In this case, we know that n = 4 (as Angel plants peppers in 4 rows), a = 1 (since Angel plants one pepper in the first row), and d = 1 (as the increment is one additional pepper per row).
Plugging in these values into the formula:
Sum = (4/2) * (2*1 + (4-1)*1)
= (2) * (2 + 3)
= 2 * 5
= 10
Therefore, Angel has a total of 10 pepper plants.