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Home » Lateral surface area = π × radius × slant height = π × 4 × 5 = 20π cm² - High Altitude Science

Lateral surface area = π × radius × slant height = π × 4 × 5 = 20π cm² - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 The sum of the first n terms of a geometric sequence is given by \( S_n = 3^n - 1 \). Find the 5th term of the sequence.

📌 The general formula for the sum of the first n terms is \( S_n = a \frac{r^n - 1}{r - 1} \).

📌 Compare \( S_n = 3^n - 1 \) with the geometric sum formula. This suggests \( r = 3 \) and \( a = 2 \), since \( 3^n - 1 = 2 \cdot \frac{3^n - 1}{3 - 1} \).

📌 Thus, the sequence has first term \( a_1 = 3^1 - 1 = 2 \) and common ratio \( r = 3 \).

📌 The nth term of a geometric sequence is \( a_n = a \cdot r^{n-1} = 2 \cdot 3^{n-1} \).

📌 So, the 5th term is \( a_5 = 2 \cdot 3^{4} = 2 \cdot 81 = 162 \).

📌 A committee of 4 people is to be chosen from 6 men and 5 women. What is the probability that the committee includes at least 2 women?

📌 Total ways to choose 4 from 11: \( \binom{11}{4} = 330 \).

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