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In the sequence above, the first 3 terms repeat without end. What is t
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18 May 2023, 10:53
18 May 2023, 10:53
Expert Reply
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Question Stats:
81% (00:55) correct
18% (01:22) wrong based on 11 sessions
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−2, 3, −5, −2, 3, −5, −2, 3, −5,…
In the sequence above, the first 3 terms repeat without end. What is the product of the 81st term through the 85th term?
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In the sequence above, the first 3 terms repeat without end. What is the product of the 81st term through the 85th term?
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300
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Re: In the sequence above, the first 3 terms repeat without end. What is t
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19 May 2023, 02:27
19 May 2023, 02:27
Answer is 300
Re: In the sequence above, the first 3 terms repeat without end. What is t
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28 May 2023, 02:01
28 May 2023, 02:01
Expert Reply
OE
There are 3 terms in the sequence and they repeat. The question asks about the product of the 81st, 82nd, 83rd, 84th, and 85th term. Use the fact that the values of the terms in the sequence repeat after every third term to determine the value of the 81st term. Divide 81 by 3 to find that there are 27 complete iterations of the sequence. The 81st term is at the end of one of these repetitions, so its value is −5. Therefore, the 82nd term is −2, the 83rd is 3, the 84th is −5, and the 85th is −2. Therefore, the product is (−5) × (−2) × 3 × (−5) × (−2) = 300. The correct answer is 300.
There are 3 terms in the sequence and they repeat. The question asks about the product of the 81st, 82nd, 83rd, 84th, and 85th term. Use the fact that the values of the terms in the sequence repeat after every third term to determine the value of the 81st term. Divide 81 by 3 to find that there are 27 complete iterations of the sequence. The 81st term is at the end of one of these repetitions, so its value is −5. Therefore, the 82nd term is −2, the 83rd is 3, the 84th is −5, and the 85th is −2. Therefore, the product is (−5) × (−2) × 3 × (−5) × (−2) = 300. The correct answer is 300.
