Question

Срочно решить))) Пожалуйста))1) Третий член арифметической прогрессии на 12 меньше шестого. Сумма второго и восьмого члено равна 4. Найдите второй и третий члены этой прогрессии. 2) Найдите сумму всех двузнаяных чисел, дающих при делении на 4 в остатке 3.Благодарю)))*

Answer 1

1)
a3+12=a6
a2+a8=4
a2+d+12=a2+4d

3d=12

d=4

a2+a2+6d=4

2a2=4-6d

2a2=4-24

a2=-10

a3=a2+d

a3=-6

 

Answer 2

Arithmetic Progression Problem

To solve the given problem, we'll first find the third member of the arithmetic progression and then use the given information to find the second and third members of the progression.

Step 1: Find the Third Member of the Arithmetic Progression

Let's assume the first member of the arithmetic progression is denoted by a, and the common difference is denoted by d. Then, the third member of the arithmetic progression can be represented as a + 2d.

Given that the third member is 12 less than the sixth member, we can write the equation as: a + 5d = (a + 2d) - 12

Solving this equation will give us the value of d.

Step 2: Find the Second and Third Members of the Progression

Once we have the value of d, we can use it to find the second and third members of the progression.

Step 3: Find the Sum of Binary Numbers Divisible by 4 with Remainder 3

To find the sum of all two-digit binary numbers that give a remainder of 3 when divided by 4, we can list the binary numbers and sum them up.

Let's start by solving the arithmetic progression problem first.

Solution

Step 1: Find the Third Member of the Arithmetic Progression

Let's assume the first member of the arithmetic progression is denoted by a, and the common difference is denoted by d.

The equation representing the third member of the arithmetic progression is: a + 2d

Given that the third member is 12 less than the sixth member, we can write the equation as: a + 5d = (a + 2d) - 12

This equation can be simplified to: 3d = -12

Solving for d: d = -4

Step 2: Find the Second and Third Members of the Progression

Now that we have the value of d, we can find the second and third members of the progression.

The second member can be represented as: a + d

The third member can be represented as: a + 2d

Given that the sum of the second and eighth members of the progression is 4, we can write the equation as: (a + d) + (a + 7d) = 4

Substituting the value of d: (a - 4) + (a - 28) = 4 2a - 32 = 4 2a = 36 a = 18

So, the second member is 18 - 4 = 14 and the third member is 18 - 8 = 10.

Step 3: Find the Sum of Binary Numbers Divisible by 4 with Remainder 3

To find the sum of all two-digit binary numbers that give a remainder of 3 when divided by 4, we can list the binary numbers and sum them up.

The binary numbers that give a remainder of 3 when divided by 4 are: 11, 1011, 1111.

Summing these binary numbers: 11 + 1011 + 1111 = 10101

So, the sum of all two-digit binary numbers that give a remainder of 3 when divided by 4 is 10101.