Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 3012:30 AM EDT
-01:30 AM EDT
Struggling to find the right strategies to score a 99 %ile on GMAT Focus? Riya (GMAT 715) boosted her score by 100-points in just 15 days! Discover how the right mentorship, tailored strategies, and an unwavering mindset can transform your GMAT prep.
May 2110:00 AM EDT
-11:59 PM EDT
Make the most of your break with the most realistic GMAT™ prep. Take up to $700 off select products.
May 2910:00 AM IST
-11:00 PM IST
Start your journey with a fully customized action plan and work with a dedicated mentor to achieve a 735+ score.
May 3101:00 AM EDT
-02:00 AM EDT
Looking for your GMAT motivation to break through the score plateau? Pragati improved her score by massive 160 points with strategic guidance and hard-work! Find out how personalized mentorship and a strong mindset can turn GMAT struggles into success.
May 3102:00 PM PDT
-03:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Jun 1006:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
11 Oct 2024, 17:27
Kudos
Bookmarks
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% (01:34) correct
21%
(01:30)
wrong
based on 839
sessions
History
Date
Time
Result
Not Attempted Yet
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 |
ShowHide Answer
Official Answer
4th
term: 24 8th
term: 384
term: 24 8th
term: 384
12 Oct 2024, 10:00
Kudos
Bookmarks
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
Kudos
Bookmarks
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.
