Question

27+24.5+22+...+х=157.5

Answer 1

Это арифметическая прогрессия
a1=27
a2=24,5  => d=24,5-27 = -2,5

сумма x членов = 157,5

S=[a1+an]*0,5 * n
S=[2*a1+d(n-1)]*0,5 * n
157,5 = [2*27 -2,5(n-1) ] *0,5 *n
315 = [54 -2,5n+2,5 ]*n
315 = (56,5 -2.5n) *n
2.5 n^2 -56.5n +315 =0
D = 56.5^2 - 315*4*2.5 = 42.25
√D = 6.5

n1= [56.5+6.5]/ (2*2.5)  = 12.6
 n1 не является натуральным поэтому не подходит
n2 = [56.5-6.5]/ 5  = 10

x=10 членом
a10 = 27 -2.5(9) = 4.5

Answer 2

To find the value of "x" in the equation:

27 + 24.5 + 22 + ... + x = 157.5

You're adding a series of numbers and trying to find the value of x. This is an arithmetic series, where each term is obtained by adding a fixed difference to the previous term. The common difference in this series is (24.5 - 27) = -2.5.

To find the value of x, you can use the formula for the sum of an arithmetic series:

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

Where:

• S is the sum of the series (in this case, 157.5).
• n is the number of terms.
• a is the first term (27).
• d is the common difference (-2.5).

We need to solve for n (the number of terms) in this equation, but we don't know the value of n yet. However, we can create a new equation by plugging in the values we have:

157.5 = (n/2)[2(27) + (n-1)(-2.5)]

Now, you can solve this equation for n:

157.5 = (n/2)[54 - 2.5n + 2.5]

157.5 = (n/2)[56.5 - 2.5n]

Now, simplify:

315 = n[56.5 - 2.5n]

Divide both sides by 315:

n(56.5 - 2.5n) = 315

56.5n - 2.5n^2 = 315

Rearrange it as a quadratic equation:

2.5n^2 - 56.5n + 315 = 0

Now, you can solve this quadratic equation for n. You can use the quadratic formula:

n = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2.5, b = -56.5, and c = 315. Plug these values into the quadratic formula to find the two possible values of n. One of these values is the number of terms in your series:

n = (-(-56.5) ± √((-56.5)^2 - 4(2.5)(315))) / (2(2.5))

n = (56.5 ± √(3180.25 - 3150)) / 5

n = (56.5 ± √30.25) / 5

Now, calculate the two possible values for n:

n₁ = (56.5 + √30.25) / 5 n₂ = (56.5 - √30.25) / 5

n₁ ≈ 8.75 n₂ ≈ 1.75

Since the number of terms must be a positive integer, n = 8.75 is not a valid solution. So, the number of terms is approximately 1.75. This doesn't make sense in the context of this series. It seems that there might be an issue with the given equation or values. Please double-check the numbers and equation for accuracy.