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

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Joined: 02 Sep 2009
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Let x1, x2, x3......xn be a sequence of positive numbers where X1 = 1,  [#permalink]

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18 Oct 2019, 03:04
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Difficulty:

15% (low)

Question Stats:

84% (01:32) correct 16% (01:40) wrong based on 32 sessions

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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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Re: Let x1, x2, x3......xn be a sequence of positive numbers where X1 = 1,  [#permalink]

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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]

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18 Oct 2019, 04:50
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]

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22 Oct 2019, 21:58

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.

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