In an arithmetic sequence, a₄ = 21 and a₁₀ = 57. What is its nth term?
Answer and explanation
Correct answer: 6n − 3
The governing concept is the nth-term formula for an arithmetic progression, aₙ = a₁ + (n − 1)d. Since a₁₀ − a₄ spans six equal steps, 57 − 21 = 36 = 6d, so the common difference is d = 6. Moving backward three steps from a₄ to a₁ gives a₁ = 21 − 3(6) = 3. Therefore aₙ = 3 + (n − 1)6 = 6n − 3. Direct checks give a₄ = 24 − 3 = 21 and a₁₀ = 60 − 3 = 57. Option B has the wrong first term, option C has the wrong common difference, and option D gives a₄ = 21 but fails at a₁₀.
Frequently asked questions
What is the correct answer to this question?
6n − 3
Why is this the correct answer?
The governing concept is the nth-term formula for an arithmetic progression, aₙ = a₁ + (n − 1)d. Since a₁₀ − a₄ spans six equal steps, 57 − 21 = 36 = 6d, so the common difference is d = 6. Moving backward three steps from a₄ to a₁ gives a₁ = 21 − 3(6) = 3. Therefore aₙ = 3 + (n − 1)6 = 6n − 3. Direct checks give a₄ = 24 − 3 = 21 and a₁₀ = 60 − 3 = 57. Option B has the wrong first term, option C has the wrong common difference, and option D gives a₄ = 21 but fails at a₁₀.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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