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11 Oct 2024, 17:27
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4th
term: 24 8th
term: 384
term: 24 8th
term: 384
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
79% (01:35) correct
21%
(01:31)
wrong
based on 819
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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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Official Answer
4th
term: 24 8th
term: 384
term: 24 8th
term: 384
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.
5. So, our answer will be: 4th term - 24 and 8th term - 384.
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.
19 Mar 2026, 19:58
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Let's walk through this step by step.
What we know: Each term in the sequence is exactly twice the previous term. This is a geometric sequence with a common ratio of 2.
Step 1: Find the relationship between the 4th and 8th terms.
Starting from the 4th term, let's see how we reach the 8th term:
- 5th term = 2 × (4th term)
- 6th term = 2 × (5th term) = 4 × (4th term)
- 7th term = 2 × (6th term) = 8 × (4th term)
- 8th term = 2 × (7th term) = 16 × (4th term)
Key Insight: 8th term = 16 × (4th term).
Step 2: Test each choice as the 4th term and see if 16 times that value appears in the list.
- If 4th term = 3, then 8th term = 3 × 16 = 48 → Not in the list
- If 4th term = 24, then 8th term = 24 × 16 = 384 → YES, 384 is in the list!
- If 4th term = 36, then 8th term = 36 × 16 = 576 → Not in the list
- If 4th term = 192, then 8th term = 192 × 16 = 3,072 → Not in the list
- If 4th term = 384, then 8th term = 384 × 16 = 6,144 → Not in the list
- If 4th term = 768, then 8th term = 768 × 16 = 12,288 → Not in the list
The only pair that works is 4th term = 24 and 8th term = 384.
Answer: 24 for the 4th term column, 384 for the 8th term column.
The big takeaway: When terms in a geometric sequence are separated by n steps, the later term equals the earlier term multiplied by (common ratio)^n. Here the 4th and 8th terms are 4 steps apart, so the multiplier is 2^4 = 16.
What we know: Each term in the sequence is exactly twice the previous term. This is a geometric sequence with a common ratio of 2.
Step 1: Find the relationship between the 4th and 8th terms.
Starting from the 4th term, let's see how we reach the 8th term:
- 5th term = 2 × (4th term)
- 6th term = 2 × (5th term) = 4 × (4th term)
- 7th term = 2 × (6th term) = 8 × (4th term)
- 8th term = 2 × (7th term) = 16 × (4th term)
Key Insight: 8th term = 16 × (4th term).
Step 2: Test each choice as the 4th term and see if 16 times that value appears in the list.
- If 4th term = 3, then 8th term = 3 × 16 = 48 → Not in the list
- If 4th term = 24, then 8th term = 24 × 16 = 384 → YES, 384 is in the list!
- If 4th term = 36, then 8th term = 36 × 16 = 576 → Not in the list
- If 4th term = 192, then 8th term = 192 × 16 = 3,072 → Not in the list
- If 4th term = 384, then 8th term = 384 × 16 = 6,144 → Not in the list
- If 4th term = 768, then 8th term = 768 × 16 = 12,288 → Not in the list
The only pair that works is 4th term = 24 and 8th term = 384.
Answer: 24 for the 4th term column, 384 for the 8th term column.
The big takeaway: When terms in a geometric sequence are separated by n steps, the later term equals the earlier term multiplied by (common ratio)^n. Here the 4th and 8th terms are 4 steps apart, so the multiplier is 2^4 = 16.
