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Home » Using the formula $ a_n = a_1 + (n-1)d $: - Sterling Industries

Using the formula $ a_n = a_1 + (n-1)d $: - Sterling Industries

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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We can confirm this by testing specific cases (like 1, 2, 3 or 2, 3, 4...
Thus, the largest integer that must divide the product of any three co...
How many lattice points lie on the line segment joining (1, 2) and (7,...
Lattice points on a line segment between two points \((x_1, y_1)\) and...
\gcd(x_2 - x_1, y_2 - y_1) + 1
where \(\gcd\) denotes the greatest common divisor.
Compute the differences:
x_2 - x_1 = 7 - 1 = 6, \quad y_2 - y_1 = 8 - 2 = 6
Compute the gcd:
\gcd(6, 6) = 6

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Expand: \( xy - x = 2y + 3 \).
Rearrange: \( xy - 2y = x + 3 \).
Factor: \( y(x - 2) = x + 3 \).
Solve for \( y \): \( y = rac{x + 3}{x - 2} \).
#### Inverse: \( f^{-1}(x) = rac{x + 3}{x - 2} \)
Evaluate the limit \( \lim_{x o 2} rac{x^2 - 4}{x - 2} \).
Factor the numerator: \( x^2 - 4 = (x - 2)(x + 2) \).
The expression becomes \( rac{(x - 2)(x + 2)}{x - 2} \).
Cancel \( x - 2 \) (for \( x
eq 2 \)): \( x + 2 \).

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