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In the arithmetic sequence

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In the arithmetic sequence  [#permalink]

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New post Updated on: 30 Dec 2018, 08:46
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In the arithmetic sequence \(t_1, t_2, t_3, . . . , t_n\) and \(t_1 = 23\) and \(t_n = t_{n - 1} - 3\) for each \(n > 1\).
What is the value of n when \(t_n = -4\)?

(A) -1
(B) 7
(C) 10
(D) 14
(E) 20

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Originally posted by Tashin Azad on 29 Dec 2018, 20:06.
Last edited by Gladiator59 on 30 Dec 2018, 08:46, edited 1 time in total.
Formatted the post and topic name.
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Re: In the arithmetic sequence  [#permalink]

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New post 29 Dec 2018, 21:39
t1=23
tn=tn-1 -3
Thus, we can see that this is an arithematic progression with -3 as the gap between 2 successive elements.
Thus, when tn= -4, d=-3 and t1=23
tn= t1+ (n-1)d
-4=23+ (n-1)*-3
this implies, n=10
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Re: In the arithmetic sequence  [#permalink]

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New post 29 Dec 2018, 22:32
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\(t_1,t_2,......t_n\)

\(t_1 = 23\)

\(t_n = t_{n-1}-3\)

first term = 23, common difference (d) = -3

\(t_n = -4\)

\(n^{th} term = a+(n-1)d\)

\(23+(n-1)(-3) = -4\)

\(23-3n+3 = -4\)

\(30 = 3n\)

\(n = 10\)

OPTION: C
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Re: In the arithmetic sequence  [#permalink]

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New post 30 Dec 2018, 08:33
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Tashin Azad wrote:
In the arithmetic sequence t1, t2, t3, . . . , tn, . . . , t1 = 23 and tn = tn - 1 - 3 for each n > 1.
What is the value of n when tn = -4 ?



(A) - 1
(B) 7
(C) 10
(D) 14
(E) 20



Gladiator59, Bunuel I think this question needs to be formatted so \(t_n = t_{n-1}-3\) :)
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Re: In the arithmetic sequence  [#permalink]

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New post 30 Dec 2018, 08:49
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Thanks for pointing out. Edited the post.

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Gladi

dave13 wrote:


Gladiator59, Bunuel I think this question needs to be formatted so \(t_n = t_{n-1}-3\) :)

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Re: In the arithmetic sequence  [#permalink]

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New post 30 Dec 2018, 22:26
Hi All,

Questions that use "sequence notation" are relatively rare on Test Day (you'll probably see just 1), but the math behind the sequence is usually some fairly simple arithmetic (add, subtract, multiply, divide).

Here, we're given the first term in the sequence (23) and we're told that each term thereafter is 3 LESS than the preceding term. Once you understand how the sequence "works", in many cases, it's really easy to just "map out" the sequence. We're asked which term in the sequence equals -4.....

1st = 23
2nd = 20
3rd = 17
4th = 14
5th = 11
6th = 8
7th = 5
8th = 2
9th = -1
10th = -4

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Re: In the arithmetic sequence  [#permalink]

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New post 31 Dec 2018, 01:12
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Re: In the arithmetic sequence   [#permalink] 31 Dec 2018, 01:12
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