Final answer:
To find the sum of the first 8 terms (S8) in an arithmetic series, we can use the formula: S8 = (n/2)(a1 + an), where n is the number of terms and a1 is the first term. In this case, a1 = 7 and a8 = 28. The common difference is found using the formula: d = (a8 - a1)/(8 - 1), and then the formula for S8 is applied.
Step-by-step explanation:
An arithmetic series is a sequence of numbers in which the difference between any two consecutive terms is constant. To find the sum of the first 8 terms (S8), we can use the formula:
S8 = (n/2)(a1 + an)
where n is the number of terms and a1 is the first term. In this case, a1 = 7 and a8 = 28.
Step 1: Find the common difference (d) using the formula: d = (a8 - a1)/(8 - 1)
d = (28 - 7)/(8 - 1) = 4
Step 2: Substitute the values into the formula for S8:
S8 = (8/2)(7 + 7 + (8 - 1)(4)) = 4(7 + 7 + 7(4)) = 4(7 + 7 + 28) = 4(42) = 168
Therefore, the sum of the first 8 terms (S8) is 168. So, the correct answer is (a) 196.