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Let x1, x2, x3......xn be a sequence of positive numbers where X1 = 1,

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Bunuel
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Let x1, x2, x3......xn be a sequence of positive numbers where X1 = 1, [#permalink] New post   18 Oct 2019, 03:04
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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
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C
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Re: Let x1, x2, x3......xn be a sequence of positive numbers where X1 = 1, [#permalink] New post   18 Oct 2019, 03:58
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Bunuel 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


\(x_{n+1} = x_n + 4\).
—> \(x_2 = x_1 + 4 = 1 + 4 = 5\).
—> \(x_3 = x_2 + 4 = 5 + 4 = 9\).

So, the given sequence would be 1, 5, 9, . . . . is in Arithmetic Progression

\(n_{th}\) term = a + (n - 1)d = 1 + (n - 1)4 = 4n - 3

IMO Option C

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Re: Let x1, x2, x3......xn be a sequence of positive numbers where X1 = 1, [#permalink] New post   18 Oct 2019, 04:50
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Bunuel 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


T1 = 1
T2 = 5
Tn = 1 + 4 (n-1) = 4n - 3

IMO C
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Re: Let x1, x2, x3......xn be a sequence of positive numbers where X1 = 1, [#permalink] New post   22 Oct 2019, 21:58
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Solution


Given:
    • \(x_1, x_2, x_3,…., x_n\) is a sequence of positive numbers
    • \(x_1 = 1\)
    • \(x_{n+1} = x_n + 4\)

To find:
    • The \(n^{th}\) term of the sequence

Approach and Working Out:
    • Given,\(x_{n+1} = x_n + 4\)
      o Implies,\(x_{n+1} - x_n = 4\)
      o Thus, we can say that all the terms of the sequence are in AP

    • \(t_n = a + (n – 1) * d\), where \(a = x_1\) and d = 4

Therefore, the nth term = 1 + (n – 1) * 4 = 4n - 3

Hence, the correct answer is Option C.

Answer: C
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Re: Let x1, x2, x3......xn be a sequence of positive numbers where X1 = 1, [#permalink] New post   20 Dec 2023, 13:32
How would you solve this if you didn't memorize the Arithmetic Progression formula?
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Re: Let x1, x2, x3......xn be a sequence of positive numbers where X1 = 1, [#permalink]
20 Dec 2023, 13:32
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