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29 Sep 2024, 03:50
Kudos
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
100% (01:30) correct
0% (00:00) wrong based on 1 sessions
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In a certain sequence of numbers, each term after the first term is found by multiplying the preceding term by 2 and then subtracting 3 from the product. If the 4th term in the sequence is 19, which of the following numbers are in the sequence?
Indicate all such numbers.
A. 5
B. 8
C. 11
D. 16
E. 22
F. 35
Indicate all such numbers.
A. 5
B. 8
C. 11
D. 16
E. 22
F. 35
10 Feb 2025, 10:57
Kudos
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OE
Since the 4th term in the sequence is 19, it follows that the 5th term is (19)(2) - 3, or 35. Proceeding backwards in the sequence from the 4th term to determine each preceding term, you would add 3 and then divide the result by 2. So the 3rd term is \(\frac{19 + 3}{2}\), or 11; the 2nd term is \(\frac{11 + 3}{2}\), or 7; and the 1st term is \(\frac{7 + 3}{2}\), or 5. Hence the first 5 terms of the sequence are 5, 7, 11, 19, and 35, of which 5, 11, and 35 are among the answer choices.
Can you show that the other three answer choices, 8, 16, and 22, are not in the sequence? Note that 8, 16, and 22 are not among the frst 5 terms of the sequence, and the 5th term of the sequence is 35. If you can show that each successive term in the sequence is greater than the term before it, you can conclude that 8, 16 and 22 are not terms in the sequence. If b is any term in the sequence, then the successive term is 2b - 3. Note that b < 2b - 3 is equivalent to b > 3, so the successive term, 2b - 3, is greater than the term before it, b, if b > 3. Since the frst term of the sequence is 5, which is greater than 3, each successive term is greater than the term before it.
Thus the correct answer consists of Choices A, C, and F.
Since the 4th term in the sequence is 19, it follows that the 5th term is (19)(2) - 3, or 35. Proceeding backwards in the sequence from the 4th term to determine each preceding term, you would add 3 and then divide the result by 2. So the 3rd term is \(\frac{19 + 3}{2}\), or 11; the 2nd term is \(\frac{11 + 3}{2}\), or 7; and the 1st term is \(\frac{7 + 3}{2}\), or 5. Hence the first 5 terms of the sequence are 5, 7, 11, 19, and 35, of which 5, 11, and 35 are among the answer choices.
Can you show that the other three answer choices, 8, 16, and 22, are not in the sequence? Note that 8, 16, and 22 are not among the frst 5 terms of the sequence, and the 5th term of the sequence is 35. If you can show that each successive term in the sequence is greater than the term before it, you can conclude that 8, 16 and 22 are not terms in the sequence. If b is any term in the sequence, then the successive term is 2b - 3. Note that b < 2b - 3 is equivalent to b > 3, so the successive term, 2b - 3, is greater than the term before it, b, if b > 3. Since the frst term of the sequence is 5, which is greater than 3, each successive term is greater than the term before it.
Thus the correct answer consists of Choices A, C, and F.
