Question

2/В последовательности 1 * * * * * * * 9 звездочками обозначены числа. Сумма любых трех соседних чисел в этой последовательности равна 15. Найдите второй член последовательности, то есть число, обозначенное первой звездочкой.1/Сундук, полный золота, весит 56 пудов, а сундук, заполненный золотом наполовину, весит 30 пудов. Сколько пудов весит пустой сундук?

Answer 1

1 5 9 1 5 9 1 5 9 1 5 9 1 5 9 1 5 9 ..................................

Answer 2

Task 2: Finding the Second Number in the Sequence

To find the second number in the sequence, we need to determine the pattern of the sequence and use the given information that the sum of any three consecutive numbers in the sequence is equal to 15.

Let's analyze the sequence:

1 * * * * * * * 9

We can see that there are 9 numbers in total, with 7 asterisks (*) representing unknown numbers. The sum of any three consecutive numbers in the sequence is equal to 15.

To find the second number in the sequence, we can set up the following equation:

x + (x+1) + (x+2) = 15

Simplifying the equation, we get:

3x + 3 = 15

Subtracting 3 from both sides, we have:

3x = 12

Dividing both sides by 3, we find:

x = 4

Therefore, the second number in the sequence, represented by the first asterisk (*), is 4.

Task 1: Weight of an Empty Chest

To find the weight of an empty chest, we can use the given information about the weight of a full chest and a chest filled halfway with gold.

Let's denote the weight of the empty chest as x.

Given: - Weight of a full chest = 56 puds - Weight of a chest filled halfway with gold = 30 puds

We can set up the following equation:

x + (56 - x)/2 = 30

Simplifying the equation, we get:

2x + 56 - x = 60

Combining like terms, we have:

x + 56 = 60

Subtracting 56 from both sides, we find:

x = 4

Therefore, the weight of the empty chest is 4 puds.