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02 Apr 2024, 03:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
47% (02:53) correct
53%
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wrong
based on 164
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After the first term in a finite sequence of numbers, each even-numbered term is created by adding 3 to the previous term, and each odd-numbered term is created by multiplying the previous term by –1. How many terms are in the sequence?
(1) The average of all terms in the sequence is \(-\frac{1}{2}\).
(2) The eighteenth term in the sequence is \(–4\).
(1) The average of all terms in the sequence is \(-\frac{1}{2}\).
(2) The eighteenth term in the sequence is \(–4\).
03 Apr 2024, 23:47
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devashish2407
Assume that the first number in the series is equal to x
We can write that series as shown below
Attachment:
Screenshot 2024-04-04 120443.png [ 50.14 KiB | Viewed 2424 times ]
Observation: In every block of 4, the sum of the terms in the block = 0
Statement 1
The average of all terms in the sequence is \(\frac{-1}{2}.\)
This statement alone doesn't help much. As the value of x is unknown, for a particular value of x we can obtain a given average.
Example: If the number of terms = 5
Average =\(\frac{ \text{The sum of the first five terms} }{ \text{Number of terms}} \)
\(\frac{-1}{2}=\frac{ \text{The sum of the first five terms} }{ \text{Number of terms}} \)
\(\frac{-1}{2}=\frac{ x }{ 5} \)
\(x = \frac{-5}{2}\)
Hence, when \(x = \frac{-5}{2}\); the number of terms = 5
Example: If the number of terms = 3
Average =\(\frac{ \text{The sum of the first three terms} }{ \text{Number of terms}} \)
\(\frac{-1}{2}=\frac{ \text{The sum of the first three terms} }{ \text{Number of terms}} \)
\(\frac{-1}{2}=\frac{ x }{ 3} \)
\(x = \frac{-3}{2}\)
Hence, when \(x = \frac{-3}{2}\); the number of terms = 3
This statement alone is not sufficient to answer the question. We can eliminate A, and D.
Statement 2
The eighteenth term in the sequence is \(–4.\)
Statement 2 alone is not sufficient. We know the value of the 18th term, however we do not know the number of terms in the sequence.
Eliminate B
Combined
From Statement 2, we can get a unique value of x.
The 18th term of the sequence = x + 3
x + 3 = -4
x = -7
From Statement 1, we know that for any unique value of x, we can find the number of terms.
As the value of x is now known, we can obtain the number of terms in the sequence.
The statements combined are sufficient to answer the question asked.
Option C
13 May 2024, 00:35
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gmatophobia
From Statement 2 we only find out the first term of the sequence right?
So how do we know what the number of terms are?
For example if the sum is -7 then n will be 14
if the sum is -11 then n will be 22
Arent there multiple values n can take?
