If aₙ = n² + dn + 2 and a₄ = 34, what is the value of d?
Answer and explanation
Correct answer: 4
Use the explicit rule at n = 4 because a₄ is given. Substitution gives a₄ = 4² + 4d + 2 = 16 + 4d + 2 = 18 + 4d. Setting this equal to 34 gives 18 + 4d = 34, so 4d = 16 and d = 4. Therefore, option C is correct. The other options result from omitting the constant 2 or making an error while solving the linear equation.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Use the explicit rule at n = 4 because a₄ is given. Substitution gives a₄ = 4² + 4d + 2 = 16 + 4d + 2 = 18 + 4d. Setting this equal to 34 gives 18 + 4d = 34, so 4d = 16 and d = 4. Therefore, option C is correct. The other options result from omitting the constant 2 or making an error while solving the linear equation.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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