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Solve the eqn: 1 + 6 + 11 + 16 + ... + x = 148

User Efi MK
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6 votes

Answer:

Explanation:

To solve the equation 1 + 6 + 11 + 16 + ... + x = 148, we need to find the value of x.

The given sequence is an arithmetic sequence with a common difference of 5.

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

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, a = 1, d = 5, and Sn = 148.

Plugging in the values, we get:

148 = (n/2)(2(1) + (n-1)(5))

Now we can solve for n by rearranging the equation and simplifying:

148 = (n/2)(2 + 5n - 5)

296 = n(2 + 5n - 5)

296 = n(5n - 3)

Now we have a quadratic equation. We can solve it by setting it equal to zero:

0 = 5n^2 - 3n - 296

Using factoring, the equation can be factored as:

0 = (5n + 37)(n - 8)

Setting each factor equal to zero, we get:

5n + 37 = 0 or n - 8 = 0

Solving for n, we find:

n = -37/5 or n = 8

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

Therefore, the value of x is 8.

User Rossco
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