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Home » Unlock Epic Profits: How to Craft the Ultimate String in Minecraft Like a Pro! - 500apps

Unlock Epic Profits: How to Craft the Ultimate String in Minecraft Like a Pro! - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 A sequence is defined by \(a_n = 3n^2 + 2n + 1\). Find the sum of the first 5 terms.

📌 \(a_1 = 3(1)^2 + 2(1) + 1 = 6\)

📌 \(a_2 = 3(2)^2 + 2(2) + 1 = 17\)

📌 \(a_3 = 3(3)^2 + 2(3) + 1 = 34\)

📌 \(a_4 = 3(4)^2 + 2(4) + 1 = 57\)

📌 \(a_5 = 3(5)^2 + 2(5) + 1 = 86\)

📌 Sum: \(6 + 17 + 34 + 57 + 86 = 200\).

📌 A cone has a radius of 3 cm and a slant height of 5 cm. Calculate the lateral surface area.

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The quadratic formula is \(x = rac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
Compute the discriminant: \((-8)^2 - 4 imes 2 imes 6 = 64 - 48 = 16\...
Then, \(x = rac{8 \pm \sqrt{16}}{4} = rac{8 \pm 4}{4}\).
So, \(x = rac{12}{4} = 3\) or \(x = rac{4}{4} = 1\).
Find the sum of the infinite geometric series with first term 5 and co...
The sum is \(rac{a}{1 - r} = rac{5}{1 - rac{1}{3}} = rac{5}{rac{2...
A box contains 5 red, 4 blue, and 3 green balls. Two balls are drawn a...
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If \( x + \frac{1}{x} = 5 \), find the value of \( x^2 + \frac{1}{x^2}...
Square both sides: \( \left(x + \frac{1}{x}\right)^2 = 25 \)
Expand: \( x^2 + 2 + \frac{1}{x^2} = 25 \)
Subtract 2: \( x^2 + \frac{1}{x^2} = 23 \)
The ratio of the ages of two people is 5:7. In 6 years, the sum of the...
Let the ages be \( 5x \) and \( 7x \).
In 6 years: \( (5x + 6) + (7x + 6) = 78 \)
Simplify: \( 12x + 12 = 78 \) → \( 12x = 66 \) → \( x = 5.5 \)
Younger age: \( 5 \times 5.5 = 27.5 \)
#### 27.5

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