Question

Найдите првый член и разность арифметической прогрессии( Аn),если:{ A5+A11=62{ A4-A1=12Варианты ответов: а) A1=4, d=3; б) A1=3, d=4; в) A1= -3, d= -4. Помогите плиззз

Answer 1

а1=3 д=4

а1+3д-а1=12

д=4

а1=31-7д

а1=3

Answer 2

Правильный вариант ответа - Б) А1=3, d=4

Answer 3

Finding the First Term and Common Difference of an Arithmetic Progression

To find the first term (A1) and the common difference (d) of an arithmetic progression, we can use the given information and solve the system of equations.

Given: - A5 + A11 = 62 - A4 - A1 = 12

Let's solve for A1 and d using the given information.

Calculating the First Term (A1) and Common Difference (d)

We can start by expressing the terms of the arithmetic progression in terms of A1 and d:

A5 = A1 + 4d A11 = A1 + 10d A4 = A1 + 3d

Now, we can use the given equations to solve for A1 and d:

A5 + A11 = 62 (A1 + 4d) + (A1 + 10d) = 62 2A1 + 14d = 62

A4 - A1 = 12 (A1 + 3d) - A1 = 12 3d = 12 d = 4

Now that we have found the value of d, we can substitute it back to find A1:

2A1 + 14(4) = 62 2A1 + 56 = 62 2A1 = 62 - 56 2A1 = 6 A1 = 3

Conclusion

Therefore, the first term (A1) of the arithmetic progression is 3 and the common difference (d) is 4. So, the correct answer is б) A1=3, d=4.