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.