Question

Арифметические прогрессии 1. В арифметической прогрессии аₙ найдите a₇ , если a₃+a₁₁=24.2. Дана арифметическая прогрессия aₙ. Известно, что a₁+a₅=10 и a₂·a₃=5. Запишите сумму первых трех ее членов.Ответы нужны в течении ближайших 20 минут!!

Answer 1

Ответ:

1. a7 = (a3+a11)/2 = 24/2 = 12

2. a3 = (a1+a5)/2 = 10/2 = 5

a2*a3 = 5 => a2 * 5 = 5 => a2 = 1

d = a3-a2 = 5 - 1 = 4

a1 = a2 - d = 1 - 4 = -3

a1 + a2 + a3 = -3 + 1 + 5 = 3

Объяснение:

Answer 2

Arithmetic Progressions

An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. The first term of an arithmetic progression is denoted as a₁, the second term as a₂, and so on. The general formula for the n-th term of an arithmetic progression is given by:

aₙ = a₁ + (n - 1)d

where d is the common difference between consecutive terms.

Question 1: Finding a₇ in an Arithmetic Progression

In this question, we are given that a₃ + a₁₁ = 24. We need to find the value of a₇.

To solve this, we can use the formula for the n-th term of an arithmetic progression. Since a₃ and a₁₁ are given, we can substitute these values into the formula and solve for a₁ and d.

Let's solve the equation step by step:

1. Substitute n = 3 into the formula to get a₃ = a₁ + 2d. 2. Substitute n = 11 into the formula to get a₁₁ = a₁ + 10d. 3. We are given that a₃ + a₁₁ = 24. Substitute the values of a₃ and a₁₁ into the equation and solve for a₁ and d.

Let's calculate the values of a₁ and d:

a₃ + a₁₁ = 24 (a₁ + 2d) + (a₁ + 10d) = 24 2a₁ + 12d = 24 a₁ + 6d = 12 ---(Equation 1)

Now, we can use the given information to solve for a₁ and d.

Please wait a moment while I calculate the values.