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Bismuth83
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A sequence is defined such that each term is twice the value of the 11 Oct 2024, 17:27
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4th
term: 24 8th
term: 384
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83% (01:32) correct 17% (01:22) wrong based on 525 sessions

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A sequence is defined such that each term is twice the value of the previous term in the sequence (so the fourth term is twice the value of the third). Which of the following could represent the 4th and 8th terms of such a sequence?
4th
term 		8th
term
3
24
36
192
384
768
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4th
term: 24 8th
term: 384
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Bismuth83
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A sequence is defined such that each term is twice the value of the 12 Oct 2024, 10:00
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1. There is a sequence such that the n+1 term is 2 times greater than the nth term. We are asked to find what could be the 4th and 8th terms.

2. Since we know none of the terms in the sequence, it's best to look at the relation between any two of them. We can notice that the mth term is \(2^{m-n}\) times greater than the nth term (assuming m > n).

3. Now, using this fact, it is known that the 8th term is \(2^{8-4} = 2^4 = 16\) times greater than the 4th term.

4. Looking at the answers, it can be noted that 192 and larger numbers cannot be possible 4th terms. So, let's check 3, 24, and 36.

  • \(3 * 16 = 48\), which isn't a possible answer for an 8th term.

  • \(24 * 16 = 384\), which is a possible answer for an 8th term.

  • \(36 * 16 = 576\), which isn't a possible answer for an 8th term.

5. So, our answer will be: 4th term - 24 and 8th term - 384.
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