Question

Послідовність (аn) арифметична прогресія.знайдіть а1 і d якщо а6= 1 ; а11= 0

Answer 1

Ответ:

Объяснение:

смотри

Answer 2

Arithmetic Progression Sequence

An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. The general form of an arithmetic progression is given by the formula a_n = a₁ + (n-1)d, where: - a_n is the nth term of the sequence - a₁ is the first term - d is the common difference between the terms - n is the position of the term in the sequence

Finding a₁ and d

Given that a₆ = 1 and a₁₁ = 0, we can use these values to find a₁ and d.

First, let's find the common difference d: - We can use the formula a_n = a₁ + (n-1)d to find the common difference. - Substituting n=6 and a₆ = 1, we get: 1 = a₁ + 5d. - Substituting n=11 and a₁₁ = 0, we get: 0 = a₁ + 10d.

By solving these two equations simultaneously, we can find the values of a₁ and d.

Solving for a₁ and d

Using the equations: - 1 = a₁ + 5d (Equation 1) - 0 = a₁ + 10d (Equation 2)

Subtracting Equation 2 from Equation 1, we get: 1 - 0 = (a₁ + 5d) - (a₁ + 10d) which simplifies to: 1 = -5d

Solving for d, we find: d = -1/5

Substituting d = -1/5 into Equation 1, we can solve for a₁: 1 = a₁ + 5(-1/5) which simplifies to: 1 = a₁ - 1

Therefore, a₁ = 2.

Conclusion

The first term a₁ of the arithmetic progression is 2, and the common difference d is -1/5.