Question

В цирке в одном из секторов для зрителей так установлены кресла,что каждый последующий ряд содержит на одно место больше,чем предыдущий.Сколько мест в секторе,если: 1)в первом ряду 8 кресел,а рядов 22; 2)в первом ряду 10 кресел,а рядов 21;

Answer 1

Арифм. прогрессия
1. a1=8  d=1   a22=8+1*(21)=29 s22=(8+29)*22/2=407  мест
2. a1=10 d=1  a21=10+20=30    s21=(10+30)*21/2=420 мест

Answer 2

Problem Analysis

The problem states that in a circus, the seats in each subsequent row contain one more seat than the previous row. We need to determine the number of seats in a given sector based on the number of seats in the first row and the number of rows.

Solution

To find the number of seats in a sector, we can use the formula for the sum of an arithmetic series:

Sum = (n/2) * (first term + last term)

where: - Sum is the total number of seats in the sector, - n is the number of rows, - first term is the number of seats in the first row, and - last term is the number of seats in the last row.

Let's calculate the number of seats in the sector for the given scenarios.

Scenario 1: First row has 8 seats and there are 22 rows

In this scenario, the number of seats in the first row is 8 and the number of rows is 22.

Using the formula, we can calculate the number of seats in the sector as follows:

Sum = (22/2) * (8 + (8 + (22-1)))

Simplifying the equation:

Sum = 11 * (8 + 29) = 11 * 37 = 407

Therefore, there are 407 seats in the sector.

Scenario 2: First row has 10 seats and there are 21 rows

In this scenario, the number of seats in the first row is 10 and the number of rows is 21.

Using the formula, we can calculate the number of seats in the sector as follows:

Sum = (21/2) * (10 + (10 + (21-1)))

Simplifying the equation:

Sum = 10.5 * (10 + 30) = 10.5 * 40 = 420

Therefore, there are 420 seats in the sector.

Summary

Based on the given information, the number of seats in the sector is: 1) 407 seats when the first row has 8 seats and there are 22 rows. 2) 420 seats when the first row has 10 seats and there are 21 rows.

Please let me know if you need any further assistance!