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\(l = \frac403\). - Anadea

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 A geometric sequence has a first term of 3 and a common ratio of 2. What is the sum of the first 6 terms?

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

📌 Here, \( a = 3 \), \( r = 2 \), and \( n = 6 \).

📌 So, \( S_6 = 3 \frac{2^6 - 1}{2 - 1} = 3 \times (64 - 1) = 3 \times 63 = 189 \).

📌 The sum of the angles in a polygon with \( n \) sides is given by \( (n-2) \times 180^\circ \). If a polygon has 9 sides, what is the measure of each interior angle if the polygon is regular?

📌 The sum of the interior angles is \( (9-2) \times 180 = 7 \times 180 = 1260^\circ \).

📌 For a regular polygon, each interior angle is \( \frac{1260}{9} = 140^\circ \).

📌 If \( \sin(x) = \frac{3}{5} \) and \( x \) is in the first quadrant, find \( \cos(x) \).

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