Question

Сумма восемнадцати чл арифм прогрессии = 495; найти 1 член если 4 равен 11

Answer 1

Решение задачи приведено на фотографии. 

Answer 2

Arithmetic Progression Calculation

To find the 1st term of the arithmetic progression when the sum of 18 terms is 495 and the 4th term is 11, we can use the formula for the sum of an arithmetic progression and the formula for the nth term of an arithmetic progression.

The sum of the first n terms of an arithmetic progression is given by the formula: S_n = n/2 * (a_1 + a_n), where: - S_n is the sum of the first n terms, - n is the number of terms, - a_1 is the first term, - a_n is the nth term.

The nth term of an arithmetic progression is given by the formula: a_n = a_1 + (n - 1) * d, where: - a_n is the nth term, - a_1 is the first term, - n is the term number, - d is the common difference.

Calculation Steps

1. We are given that the sum of 18 terms is 495, so we can use the formula for the sum of an arithmetic progression to find the value of the first term, a_1. - 495 = 18/2 * (a_1 + a_18) 2. We are also given that the 4th term is 11, so we can use the formula for the nth term of an arithmetic progression to find the value of the first term, a_1. - a_4 = a_1 + (4 - 1) * d - 11 = a_1 + 3d

3. We can solve the system of equations formed by the two above equations to find the value of the first term, a_1.

Solution

By solving the system of equations formed by the above two equations, we can find the value of the first term, a_1. This will give us the answer to the problem.