Question

В волшебном саду в течение ста лет каждый год, кроме одного, на волшебном дереве вырастало ровно на 1 плод больше, чем в предыдущий год. А в один год была замечательная погода, и плодов на дереве выросло в 2 раза больше, чем в предыдущий год. В каком году была эта замечательная погода, если в первый год на дереве вырос 1 плод, а в сотом году выросло 152 плода?

Answer 1

На 51году...................... ..

Answer 2

Understanding the Problem

We are given a scenario about a magical garden where, for 100 years, every year except one, the magical tree grows exactly one more fruit than the previous year. However, in one particular year, the tree grows twice as many fruits as the previous year. We need to determine in which year this exceptional growth occurred, given that in the first year the tree grew 1 fruit and in the 100th year it grew 152 fruits.

Solution

To solve this problem, we can use a simple mathematical approach. Let's assume that the exceptional growth year is represented by variable x. We know that in the first year, the tree grew 1 fruit, and in the 100th year, it grew 152 fruits.

From the given information, we can deduce the following equation: - In the first year: 1 fruit - In the second year: 1 + 1 = 2 fruits - In the third year: 2 + 1 = 3 fruits - In the fourth year: 3 + 1 = 4 fruits - And so on...

We can see that the number of fruits in each year is increasing by 1. Therefore, we can represent the number of fruits in each year as a sequence of consecutive numbers: 1, 2, 3, 4, 5, ...

However, in the exceptional growth year, the tree grew twice as many fruits as the previous year. So, in the exceptional growth year, the number of fruits is twice the number of fruits in the previous year.

Using this information, we can set up the following equation to represent the number of fruits in the exceptional growth year: x + 1 = 2 * (x - 1)

Simplifying the equation, we get: x + 1 = 2x - 2

Solving for x, we find: x = 3

Therefore, the exceptional growth year is the third year.

Answer

The exceptional growth year, where the tree grew twice as many fruits as the previous year, is the third year.