Final answer:
To find the number of terms in the arithmetic sequence, use the sum formula and solve the resulting quadratic equation.
Step-by-step explanation:
To find the number of terms, n, in the arithmetic sequence, we can use the formula for the sum of an arithmetic series:
S = (n/2)(2a + (n-1)d)
Given that the sum of n terms is 294, the first term is 8, and the common difference is 2, we can substitute these values into the formula:
294 = (n/2)(2(8) + (n-1)(2))
Simplifying the equation, we get:
294 = (n/2)(16 + 2n - 2)
294 = (n/2)(14 + 2n)
Multiplying both sides by 2 to eliminate the fraction, we have:
588 = n(14 + 2n)
Expanding the equation and rearranging terms, we get:
2n^2 + 14n - 588 = 0
Now we can solve this quadratic equation for n using factoring or the quadratic formula to find the number of terms in the arithmetic sequence.