If a₁ = 80 and aₙ₊₁ = aₙ − (3n + 2), what is a₅?
Answer and explanation
Correct answer: 42
This is a recursive sequence because each term is obtained from the preceding term using the index n. Start with a₁ = 80. For n = 1, a₂ = 80 − (3×1 + 2) = 80 − 5 = 75. For n = 2, a₃ = 75 − 8 = 67. For n = 3, a₄ = 67 − 11 = 56. Finally, for n = 4, a₅ = 56 − 14 = 42. Thus the successive subtractions are 5, 8, 11, and 14, increasing by 3 each time. Option B is correct. Options A, C, and D result from an arithmetic or indexing error, such as omitting one subtraction or using the wrong value of n.
Frequently asked questions
What is the correct answer to this question?
42
Why is this the correct answer?
This is a recursive sequence because each term is obtained from the preceding term using the index n. Start with a₁ = 80. For n = 1, a₂ = 80 − (3×1 + 2) = 80 − 5 = 75. For n = 2, a₃ = 75 − 8 = 67. For n = 3, a₄ = 67 − 11 = 56. Finally, for n = 4, a₅ = 56 − 14 = 42. Thus the successive subtractions are 5, 8, 11, and 14, increasing by 3 each time. Option B is correct. Options A, C, and D result from an arithmetic or indexing error, such as omitting one subtraction or using the wrong value of n.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Recursive rule.
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