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Home » You Need This Modern Data Platform—Watch How It Transforms Your Decision-Making! - SUpost

You Need This Modern Data Platform—Watch How It Transforms Your Decision-Making! - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 A geometric sequence starts with 3 and has a common ratio of 4. What is the 6th term of the sequence?

📌 The \(n\)-th term of a geometric sequence is given by \(a_n = a \cdot r^{n-1}\), where \(a = 3\) and \(r = 4\). The 6th term is \(3 \times 4^{5} = 3 \times 1024 = 3072\).

📌 Find the sum of the first 8 terms of the arithmetic sequence where the first term is 5 and the common difference is 3.

📌 The sum \(S_n\) of the first \(n\) terms of an arithmetic sequence is given by \(S_n = \frac{n}{2} (2a + (n-1)d)\). Here, \(n = 8\), \(a = 5\), and \(d = 3\).

📌 S_8 = \frac{8}{2} (2 \times 5 + 7 \times 3) = 4 \times (10 + 21) = 4 \times 31 = 124

📌 A rocket travels at a speed of 7,800 meters per second. How long will it take to travel 1,000 kilometers?

📌 Convert 1,000 kilometers to meters: \(1,000 \times 1,000 = 1,000,000\) meters. The time taken is \(\frac{1,000,000}{7,800} \approx 128.21\) seconds.

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