Tìm x: 1 + 4 + 7 +...+ x = 176

To find the value of x, we need to determine the pattern of the series and then solve for x.

The given series is an arithmetic series with a common difference of 3. The first term is 1, and we need to find the value of x when the sum of the series is 176.

The formula for the sum of an arithmetic series is:

Sn = (n/2)(2a + (n-1)d)

Where Sn is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.

In this case, we have:

176 = (n/2)(2(1) + (n-1)(3))

Simplifying the equation:

176 = (n/2)(2 + 3n - 3)

176 = (n/2)(3n - 1)

Multiplying both sides by 2 to eliminate the fraction:

352 = n(3n - 1)

Expanding the equation:

352 = 3n^2 - n

Rearranging the equation to form a quadratic equation:

3n^2 - n - 352 = 0

Now we can solve this quadratic equation to find the value of n.

Using factoring, the equation can be factored as:

(3n + 16)(n - 22) = 0

Setting each factor equal to zero:

3n + 16 = 0 or n - 22 = 0

Solving for n in each equation:

3n = -16 or n = 22

Dividing both sides of the first equation by 3:

n = -16/3

Since the number of terms cannot be negative, we discard the negative solution.

Therefore, the value of x is 22.