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Sequence S consists of 24 nonzero integers. If each term in S after the second is product of the previous 2 terms, how many terms in S are –ve?
1) 3rd term in S is +ve
2) 4th term in S is –ve
2) 4th term in S is –ve
- a)Exactly one of the statements can answer the question
- b)Both statements are required to answer the question
- c)Each statement can answer the question individually
- d)More information is required as the information provided is insufficient to answer the question
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Sequence S consists of 24 nonzero integers. If each term in S after th...
Determined if the first two terms are given?
Let the first two terms of the sequence be $a$ and $b$. Then the third term is $a\cdot b$, the fourth term is $a\cdot b^2$, the fifth term is $a^2\cdot b^3$, the sixth term is $a^3\cdot b^5$, and so on. In general, the $n$th term is $$a^{F_{n-2}}\cdot b^{F_{n-1}},$$where $F_k$ denotes the $k$th Fibonacci number. Since $F_{23}=28657$ and $F_{24}=46368$, the $24$th term of the sequence is uniquely determined given the first two terms. Therefore, there are $\boxed{24}$ terms in the sequence.
Let the first two terms of the sequence be $a$ and $b$. Then the third term is $a\cdot b$, the fourth term is $a\cdot b^2$, the fifth term is $a^2\cdot b^3$, the sixth term is $a^3\cdot b^5$, and so on. In general, the $n$th term is $$a^{F_{n-2}}\cdot b^{F_{n-1}},$$where $F_k$ denotes the $k$th Fibonacci number. Since $F_{23}=28657$ and $F_{24}=46368$, the $24$th term of the sequence is uniquely determined given the first two terms. Therefore, there are $\boxed{24}$ terms in the sequence.
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Sequence S consists of 24 nonzero integers. If each term in S after th...
Since each term in the sequence is the product of the previous 2 terms, the sequence can be expressed as:
a, b, ab, a^2b, a^3b^2, a^5b^3, a^8b^5, ...
where a and b are the first two terms in the sequence.
To find the number of terms in the sequence, we need to find the largest power of 2 that is less than or equal to 24. This is 16.
So the sequence has 1 + 2 + 4 + 8 + 16 = 31 terms.
However, we need to subtract 7 terms from this count, since the first 7 terms are a, b, ab, a^2b, a^3b^2, a^5b^3, and a^8b^5, and the problem specifies that all terms in the sequence are nonzero. This leaves us with:
31 - 7 = 24 terms.
Therefore, there are 24 terms in the sequence S.
a, b, ab, a^2b, a^3b^2, a^5b^3, a^8b^5, ...
where a and b are the first two terms in the sequence.
To find the number of terms in the sequence, we need to find the largest power of 2 that is less than or equal to 24. This is 16.
So the sequence has 1 + 2 + 4 + 8 + 16 = 31 terms.
However, we need to subtract 7 terms from this count, since the first 7 terms are a, b, ab, a^2b, a^3b^2, a^5b^3, and a^8b^5, and the problem specifies that all terms in the sequence are nonzero. This leaves us with:
31 - 7 = 24 terms.
Therefore, there are 24 terms in the sequence S.
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Sequence S consists of 24 nonzero integers. If each term in S after the second is product of the previous 2 terms, how many terms in S are –ve?1) 3rd term in S is +ve2) 4th term in S is –vea)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer?
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Sequence S consists of 24 nonzero integers. If each term in S after the second is product of the previous 2 terms, how many terms in S are –ve?1) 3rd term in S is +ve2) 4th term in S is –vea)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Sequence S consists of 24 nonzero integers. If each term in S after the second is product of the previous 2 terms, how many terms in S are –ve?1) 3rd term in S is +ve2) 4th term in S is –vea)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sequence S consists of 24 nonzero integers. If each term in S after the second is product of the previous 2 terms, how many terms in S are –ve?1) 3rd term in S is +ve2) 4th term in S is –vea)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer?.
Sequence S consists of 24 nonzero integers. If each term in S after the second is product of the previous 2 terms, how many terms in S are –ve?1) 3rd term in S is +ve2) 4th term in S is –vea)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Sequence S consists of 24 nonzero integers. If each term in S after the second is product of the previous 2 terms, how many terms in S are –ve?1) 3rd term in S is +ve2) 4th term in S is –vea)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sequence S consists of 24 nonzero integers. If each term in S after the second is product of the previous 2 terms, how many terms in S are –ve?1) 3rd term in S is +ve2) 4th term in S is –vea)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Sequence S consists of 24 nonzero integers. If each term in S after the second is product of the previous 2 terms, how many terms in S are –ve?1) 3rd term in S is +ve2) 4th term in S is –vea)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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