In an arithmetic progression, a₃ = 11 and a₉ = 47. What is a₁?
Answer and explanation
Correct answer: −1
Use aₙ = a₁ + (n − 1)d. The two given values produce a₃ = a₁ + 2d = 11 and a₉ = a₁ + 8d = 47. Subtracting gives 6d = 36, so d = 6. Substitution into the first equation gives a₁ + 12 = 11, hence a₁ = −1. Checking the result, the progression begins −1, 5, 11, … and after six intervals of size 6 reaches a₉ = −1 + 8 × 6 = 47. Options B, C, and D do not satisfy both equations with d = 6. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
−1
Why is this the correct answer?
Use aₙ = a₁ + (n − 1)d. The two given values produce a₃ = a₁ + 2d = 11 and a₉ = a₁ + 8d = 47. Subtracting gives 6d = 36, so d = 6. Substitution into the first equation gives a₁ + 12 = 11, hence a₁ = −1. Checking the result, the progression begins −1, 5, 11, … and after six intervals of size 6 reaches a₉ = −1 + 8 × 6 = 47. Options B, C, and D do not satisfy both equations with d = 6. Therefore, option A is correct.
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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