In an arithmetic progression, a₃ = 13 and a₁₀ = 62. What is a₁?
Answer and explanation
Correct answer: −1
Use aₙ = a₁ + (n − 1)d. The difference between the tenth and third terms covers seven equal steps, so a₁₀ − a₃ = 7d. Hence 62 − 13 = 49 = 7d, giving d = 7. Now the third-term equation is 13 = a₁ + 2d = a₁ + 14. Therefore a₁ = 13 − 14 = −1, so option A is correct. Checking the sequence with a₁ = −1 and d = 7 gives −1, 6, 13, … and the tenth term is −1 + 9 × 7 = 62. Options B, C, and D fail to reproduce at least one of the two given terms.
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 difference between the tenth and third terms covers seven equal steps, so a₁₀ − a₃ = 7d. Hence 62 − 13 = 49 = 7d, giving d = 7. Now the third-term equation is 13 = a₁ + 2d = a₁ + 14. Therefore a₁ = 13 − 14 = −1, so option A is correct. Checking the sequence with a₁ = −1 and d = 7 gives −1, 6, 13, … and the tenth term is −1 + 9 × 7 = 62. Options B, C, and D fail to reproduce at least one of the two given terms.
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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