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Let x1, x2, x3......xn be a sequence of positive numbers whe
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10 Feb 2020, 09:50
10 Feb 2020, 09:50
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Let \(x_1, x_2, x_3......x_n\) be a sequence of positive numbers where \(x_1 = 1\), and \(x_{n+1} = x_n + 4\). What represents the \(n_{th}\) term in the sequence?
A. \(-3n\)
B. \(3n - 4\)
C. \(4n - 3\)
D. \(4n - 4\)
E. \(5n\)
Kudos for the right answer and explanation
A. \(-3n\)
B. \(3n - 4\)
C. \(4n - 3\)
D. \(4n - 4\)
E. \(5n\)
Kudos for the right answer and explanation
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Re: Let x1, x2, x3......xn be a sequence of positive numbers whe
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10 Feb 2020, 10:02
10 Feb 2020, 10:02
1
Carcass wrote:
Let \(x_1, x_2, x_3......x_n\) be a sequence of positive numbers where \(x_1 = 1\), and \(x_{n+1} = x_n + 4\). What represents the \(n_th\) term in the sequence?
A. \(-3n\)
B. \(3n - 4\)
C. \(4n - 3\)
D. \(4n - 4\)
E. \(5n\)
Kudos for the right answer and explanation
A. \(-3n\)
B. \(3n - 4\)
C. \(4n - 3\)
D. \(4n - 4\)
E. \(5n\)
Kudos for the right answer and explanation
\(x_1 = 1\)
\(x_{n+1} = x_n + 4\)
The easiest way is to plugin \(n = 1\) in the options (to get the 1st term): Only Option C gives the value as 1, which matches with the given value.
Answer C
Alternate:
\(x_1 = 1\)
\(x_{n+1} = x_n + 4\)
For \(n = 1\): \(x_{1+1} = x_1 + 4 => x_2 = 1 + 4 = 5\)
For \(n = 2\): \(x_{2+1} = x_2 + 4 => x_3 = 5 + 4 = 9\)
Thus, each term (from the 2nd term onward) is 4 more than the previous term; the series being: 1, 5, 9, 13, ...
It is clear that each term is 3 less than a multiple of 4 --- Option C
Re: Let x1, x2, x3......xn be a sequence of positive numbers whe
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10 Mar 2023, 09:08
10 Mar 2023, 09:08
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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