Sequences and Series

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Q1. What is the common difference in the sequence 3, 7, 11, 15, ...?

Solution:

The common difference is found by subtracting the first term from the second: 7 - 3 = 4.

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Q2. What is the solution to the inequality 5x + 2 ≥ 12?

Solution:

Subtract 2 from both sides: 5x ≥ 10. Then divide by 5: x ≥ 2.

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Q3. Which of the following is a solution to the equation 4x - 7 = 5?

Solution:

Add 7 to both sides: 4x = 12. Then divide by 4: x = 3.

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Q4. Which of the following represents the inequality x + 5 > 2?

Solution:

Subtract 5 from both sides: x > -3.

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Q5. What is the solution to the equation 4x - 2 = 2x + 6?

Solution:

Subtract 2x from both sides: 2x - 2 = 6. Then add 2: 2x = 8. Finally, divide by 2: x = 4.

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Q6. Which of the following is a solution to the equation 4x + 1 = 13?

Solution:

Subtract 1 from both sides: 4x = 12. Then divide by 4: x = 3.

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Q7. Which of the following is a solution to the equation x^2 + 2x - 8 = 0?

Solution:

Factor the equation: (x + 4)(x - 2) = 0. The solutions are x = -4 and x = 2.