If an arithmetic progression has a₄ = 17 and d = 4, what is the first term a₁?
Answer and explanation
Correct answer: 5
The governing concept is the general term of an arithmetic progression: aₙ = a₁ + (n − 1)d. For the fourth term, a₄ = a₁ + 3d. Substituting the given values gives 17 = a₁ + 3(4) = a₁ + 12. Therefore, a₁ = 17 − 12 = 5, so option A is correct. This can also be checked by moving backward through the progression: 17 is the fourth term, so the third term is 13, the second is 9, and the first is 5. Options B, C, and D result from subtracting the wrong number of common differences or using an incorrect difference.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The governing concept is the general term of an arithmetic progression: aₙ = a₁ + (n − 1)d. For the fourth term, a₄ = a₁ + 3d. Substituting the given values gives 17 = a₁ + 3(4) = a₁ + 12. Therefore, a₁ = 17 − 12 = 5, so option A is correct. This can also be checked by moving backward through the progression: 17 is the fourth term, so the third term is 13, the second is 9, and the first is 5. Options B, C, and D result from subtracting the wrong number of common differences or using an incorrect difference.
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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