Question

Новогодняя гирлянда составлена из красных и жёлтых лампочек, которые идут в таком порядке: одна красная, две жёлтых, три красных, четыре жёлтых, пять красных, шесть жёлтых и т. д. Всего в гирлянде 36 лампочек. Сколько всего красных лампочек в этой гирлянде?

Answer 1

36:2=16 лампочек красных

Answer 2

Calculation of the Number of Red Bulbs in the Garland

To determine the total number of red bulbs in the garland, we need to analyze the pattern of alternating red and yellow bulbs. The pattern is as follows: one red bulb, two yellow bulbs, three red bulbs, four yellow bulbs, five red bulbs, six yellow bulbs, and so on. The garland consists of a total of 36 bulbs.

To find the number of red bulbs, we can observe that the number of bulbs in each group (one red bulb and the corresponding number of yellow bulbs) is increasing by one each time. Therefore, we can calculate the number of red bulbs by finding the sum of the natural numbers up to a certain point.

Let's break down the calculation step by step:

1. Determine the number of groups of bulbs in the garland: - Each group consists of one red bulb and a certain number of yellow bulbs. - The number of bulbs in each group increases by one each time. - We need to find the number of groups that add up to a total of 36 bulbs.

2. Calculate the number of red bulbs: - The number of red bulbs is equal to the sum of the natural numbers up to the number of groups. - We can use the formula for the sum of the first n natural numbers: sum = (n * (n + 1)) / 2.

Let's calculate the number of red bulbs in the garland:

1. Determine the number of groups of bulbs: - We need to find the number of groups that add up to a total of 36 bulbs. - By observation, we can see that the sum of the first n natural numbers is equal to the total number of bulbs in the garland. - We can use trial and error or a simple calculation to find the number of groups that add up to 36 bulbs.

After calculating, we find that the number of groups is 8.

2. Calculate the number of red bulbs: - We can use the formula for the sum of the first n natural numbers: sum = (n * (n + 1)) / 2. - Substituting the value of n as 8, we can calculate the sum of the first 8 natural numbers, which will give us the number of red bulbs.

Using the formula, we find that the sum of the first 8 natural numbers is 36.

Therefore, the garland consists of a total of 36 red bulbs.

Please note that the calculation is based on the given pattern and assumption that the pattern continues in the same way throughout the garland.