Question

Знайдіть суму всіх додатних членів арифметичної прогресії 8,4; 7,8; 7,2;…

Answer 1

Ответ:

63

Объяснение:

1)найдём d:

7,8-8,4=-0,6

2)найдём чему будет равно n, когда аn = 0:

0= 8,4-0,6(n-1)

8,4-0,6n+0,6=0

0,6n=9

n=15 → всего 14 положительных членов арифметической прогресии, значит нужно искать S14, найдём же!

$S_{n} = \frac{2a_{1} + d(n -1) }{2} \times n \\ S_{14} = \frac{2 \times 8.4 - 0.6(14 - 1)}{2} \times 14 = (16.8 - 0.6 \times 13) \times 7 = (16.8 - 7.8) \times 7 = 9 \times 7 = 63$

Answer 2

Calculating the Sum of an Arithmetic Progression

To find the sum of all the positive members of the arithmetic progression 8.4, 7.8, 7.2, ... we can use the formula for the sum of an arithmetic progression.

The formula for the sum of the first n terms of an arithmetic progression is given by:

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

Applying the Formula

Using the given arithmetic progression, we can calculate the sum of the first n terms by finding the value of n and the value of a_n.

From the provided information, we have: - a_1 = 8.4 - a_2 = 7.8 - a_3 = 7.2

We can use the formula to find the sum of the first 3 terms, as follows:

S_3 = 3/2 * (8.4 + 7.2)

Calculating the Sum

Now, let's calculate the sum:

S_3 = 3/2 * (8.4 + 7.2) = 3/2 * 15.6 = 23.4

So, the sum of the first 3 positive terms of the given arithmetic progression is 23.4.

Conclusion

The sum of all the positive members of the arithmetic progression 8.4, 7.8, 7.2 is 23.4.