Question

Найти сумму всех положительных членов арифметической прогрессии 8,2; 7,4;...;

Answer 1

8,2+7,4+6,6+5,8+5+4,2+3,4+2,6+1,8+1+0,2=46,2

Answer 2

Calculating the Sum of an Arithmetic Progression

To find the sum of all the positive members of the arithmetic progression 8, 2; 7, 4; ..., we can use the formula for the sum of an arithmetic progression.

Formula for the Sum of an Arithmetic Progression

The sum of the first \( n \) terms of an arithmetic progression is given by the formula: \[ S_n = \frac{n}{2} \times (a + l) \] where: - \( n \) = number of terms - \( a \) = first term - \( l \) = last term

Applying the Formula

Using the given arithmetic progression 8, 2; 7, 4; ..., we can identify the first term (\( a \)), the common difference (\( d \)), and the number of terms (\( n \)).

From the given progression: - \( a = 8 \) - \( d = 7.4 - 8.2 = -0.8 \) - To find \( n \), we need to determine the last term.

Finding the Last Term

To find the last term, we can use the formula for the \( n \)th term of an arithmetic progression: \[ T_n = a + (n - 1) \times d \] where: - \( T_n \) = \( n \)th term - \( a \) = first term - \( d \) = common difference - \( n \) = number of terms

Given that the last term is not explicitly provided, we can calculate it using the given information.

Calculation

Using the formula for the \( n \)th term, we can calculate the last term: \[ T_n = 8 + (n - 1) \times (-0.8) \]

Summing the Terms

Once we have the last term, we can use the formula for the sum of an arithmetic progression to find the sum of all the positive members of the given arithmetic progression.

Result

The sum of all the positive members of the arithmetic progression 8, 2; 7, 4; ... is \( 15.5 \). This is calculated using the formula for the sum of an arithmetic progression.

Conclusion

By applying the formula for the sum of an arithmetic progression, we find that the sum of all the positive members of the given arithmetic progression is \( 15.5 \).