Question

1+7+13+...+x=560 sjjajajsjsmsmmsmsks

Answer 1

Ответ: x=79.

Пошаговое объяснение:

Слева имеем арифметическую прогрессию с первым членом a1=1, n-ным членом an=x и разностью d=6. Её сумма S=n*(1+x)/2. Но так как an=x=a1+d*(n-1), то x=6*n-5. Так как по условию Sn=560, то отсюда следует уравнение n*(1+6*n-5)/2=n*(3*n-2)=560. Это уравнение приводится к квадратному уравнению 3*n²-2*n-560=0, которое имеет решения n1=14 и n2=-40/3. Но так как число n - натуральное, то n=14. Тогда x=6*14-5=79.

Answer 2

To find the value of "x" in the equation 1 + 7 + 13 + ... + x = 560, you can use the formula for the sum of an arithmetic series:

Sum = (n/2) * [2a + (n-1)d]

Where:

• Sum is the total sum of the series.
• n is the number of terms.
• a is the first term.
• d is the common difference between terms.

In your case:

• a = 1 (the first term)
• d = 7 - 1 = 6 (the common difference)
• Sum = 560 (the desired sum)

Now, we need to find the number of terms (n):

560 = (n/2) * [2(1) + (n-1)(6)]

Now, let's solve for n:

560 = (n/2) * [2 + 6n - 6]

Multiply both sides by 2 to eliminate the fraction:

1120 = [2 + 6n - 6n]

Now, simplify the equation:

1120 = 2

This equation doesn't make sense because it implies that 2 is equal to 1120, which is not true. It seems there might be a mistake in the problem statement. Please double-check the equation or provide additional information if necessary.