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Home » Real Eyes Wait—Here’s How Every Lie Crumbles Under the Weight of Truth! - American Beagle Club

Real Eyes Wait—Here’s How Every Lie Crumbles Under the Weight of Truth! - American Beagle Club

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 $$Question: How many numbers are in the list \( 3, 8, 13, \ldots, 98 \)?

📌 Solution: The given sequence is an arithmetic sequence with the first term \( a = 3 \) and common difference \( d = 5 \). The general term of the sequence is given by:

📌 a_n = a + (n-1) \cdot d = 3 + (n-1) \cdot 5

📌 We need to find \( n \) such that \( a_n = 98 \):

📌 + (n-1) \cdot 5 = 98

📌 Subtract 3 from both sides:

📌 Divide by 5:

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\[ \lambda = rac{7 \pm \sqrt{(-7)^2 - 4 \cdot 1 \cdot 10}}{2 \cdot 1}...
\[ \lambda = rac{7 \pm \sqrt{49 - 40}}{2} \]
\[ \lambda = rac{7 \pm \sqrt{9}}{2} \]
\[ \lambda = rac{7 \pm 3}{2} \]
The eigenvalues are:
\( \lambda = rac{10}{2} = 5 \)
\( \lambda = rac{4}{2} = 2 \)
The eigenvalues are 5 and 2.
#### 5, 2
Determine the convergence or divergence of the series \( \sum_{n=1}^{\...

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