What are the first term and common difference of aₙ = 12 − 7(n − 1)?
Answer and explanation
Correct answer: a₁ = 12, d = −7
Use the standard nth-term form of an arithmetic progression: aₙ = a₁ + (n − 1)d. Compare it with the given expression aₙ = 12 − 7(n − 1), or write it as aₙ = 12 + (n − 1)(−7). The comparison immediately gives a₁ = 12 and d = −7. Direct checking confirms this: for n = 1, a₁ = 12 − 7(0) = 12; for n = 2, a₂ = 12 − 7 = 5, and a₂ − a₁ = 5 − 12 = −7. Thus option C is correct. Option A loses the negative sign, option B incorrectly calls the second term the first, and option D reverses the roles of the first term and the difference.
Frequently asked questions
What is the correct answer to this question?
a₁ = 12, d = −7
Why is this the correct answer?
Use the standard nth-term form of an arithmetic progression: aₙ = a₁ + (n − 1)d. Compare it with the given expression aₙ = 12 − 7(n − 1), or write it as aₙ = 12 + (n − 1)(−7). The comparison immediately gives a₁ = 12 and d = −7. Direct checking confirms this: for n = 1, a₁ = 12 − 7(0) = 12; for n = 2, a₂ = 12 − 7 = 5, and a₂ − a₁ = 5 − 12 = −7. Thus option C is correct. Option A loses the negative sign, option B incorrectly calls the second term the first, and option D reverses the roles of the first term and the difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..
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