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Home » Discover the Surprising Answer to Where Singapore Truly Lives—Listen Up! - Anadea

Discover the Surprising Answer to Where Singapore Truly Lives—Listen Up! - Anadea

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Solution: Let the first term of the arithmetic sequence be $ a $ and the common difference be $ d $. The sequence has 8 terms, so the sum $ S_8 $ is:

📌 The eighth term is $ a + 7d $, and the first term is $ a $, so their sum is:

📌 Now solve the system. From equation (2): $ 2a + 7d = 112 $. Multiply both sides by 4:

📌 This matches equation (1), so the equations are consistent. Now use $ 2a + 7d = 112 $ to express $ a $ in terms of $ d $:

📌 For $ a $ to be real and $ d $ to be rational (and likely integer in such models), $ d $ must be even. Let $ d = 2k $. Then:

📌 Now verify sum: $ 8a + 28d = 8(56 - 7k) + 28(2k) = 448 - 56k + 56k = 448 $, which holds.

📌 But from equation (2): $ 2a + 7d = 112 $, substitute $ a = 56 -

📌 But notice: $ 8a + 28d = 4(2a + 7d) = 4 imes 112 = 448 $, which is always true. Thus, the system is dependent, but we can pick values. However, we must find $ d $, so re-express.

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