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In an Arithmetic Series: If a1 = 7 and a8 = 28, find S8

a) 196
b) 140
c) 112
d) 84

1 Answer

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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.

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