In the sequence (120, 117, 111, 102, 90, ...), the differences are (-3, -6, -9, -12, ...). What will be the next term?
Answer and explanation
Correct answer: 75
The governing concept is a recursive difference pattern. The listed successive differences are -3, -6, -9, and -12; each difference decreases by 3, so the next difference must be -15. The last displayed term is 90. Applying the next difference gives 90 + (-15) = 75, or equivalently 90 - 15 = 75. Thus option A is correct. The sequence is not an arithmetic progression because its term-to-term differences are not constant; instead, the differences themselves form an arithmetic progression. Options B, C, and D would correspond to subtracting 12, 9, or 6 again, rather than continuing the stated difference pattern by subtracting the next multiple of 3.
Frequently asked questions
What is the correct answer to this question?
75
Why is this the correct answer?
The governing concept is a recursive difference pattern. The listed successive differences are -3, -6, -9, and -12; each difference decreases by 3, so the next difference must be -15. The last displayed term is 90. Applying the next difference gives 90 + (-15) = 75, or equivalently 90 - 15 = 75. Thus option A is correct. The sequence is not an arithmetic progression because its term-to-term differences are not constant; instead, the differences themselves form an arithmetic progression. Options B, C, and D would correspond to subtracting 12, 9, or 6 again, rather than continuing the stated difference pattern by subtracting the next multiple of 3.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
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