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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # In a certain sequence of numbers, each term after the first.  Question banks Downloads My Bookmarks Reviews Important topics
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Intern Joined: 02 Dec 2015
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In a certain sequence of numbers, each term after the first. [#permalink] 00:00

Question Stats: 6% (00:33) correct 93% (00:45) wrong based on 44 sessions
In a certain sequence of numbers, each term after the first term is found by multiplying the preceding term by 2 and then subtracting 3 from the product. If the 4th term in the sequence is 19, which of the following numbers are in the sequence? Indicate all such numbers.

A.5
B.8
C.11
D.16
E.22
F.35

[Reveal] Spoiler:
a,c,f
[Reveal] Spoiler: OA Retired Moderator Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Re: In a certain sequence of numbers, each term after the first. [#permalink]
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Expert's post
maverickjin8 wrote:
In a certain sequence of numbers, each term after the first term is found by multiplying the preceding term by 2 and then subtracting 3 from the product. If the 4th term in the sequence is 19, which of the following numbers are in the sequence? Indicate all such numbers.

A.5
B.8
C.11
D.16
E.22
F.35

I don't know how to solve this in a proper way.

Let the first term be $$x$$. then the series is....

$$X$$, $$2X -3$$, $$4X - 9$$, $$8X - 21$$

8X -21 =19
8X =40
X =5

So putting X =5 the series is 5, 7, 11, 19, 35, 67...............

So 5, 11 and 35..

PS: this question is very strangely worded! Can you share the source?
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Intern Joined: 10 Jun 2018
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Re: In a certain sequence of numbers, each term after the first. [#permalink]
The 4th term is 19.
5th term is (19*2)-3 = 35

the 3rd term is (19+3)/2 = 11

similarly 2nd and 1st term is respectively 7 and 5.

Intern Joined: 17 Dec 2018
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Re: In a certain sequence of numbers, each term after the first. [#permalink]
sandy wrote:
PS: this question is very strangely worded! Can you share the source?

ETS Official Quantitative Reasoning Practice Questions, Chapter 7, Practice Set 1, Question 19 Intern Joined: 02 Aug 2019
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Re: In a certain sequence of numbers, each term after the first. [#permalink]
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I quickly came up with the formula: 2x - 3 = current term (where x = preceding term):

So 2x - 3 = 19
2x = 22
x = 11 --> C

2x - 3 = 11
2x = 14
x = 7

2x - 3 = 7
2x = 10
x =5 --> A

The next term in the sequence would be --> 2x - 3 = 2(19) - 3 = 35 --> F

Therefore, the answer is A, C, F
Intern Joined: 18 Jul 2019
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Re: In a certain sequence of numbers, each term after the first. [#permalink]
c Intern Joined: 19 Oct 2019
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Re: In a certain sequence of numbers, each term after the first. [#permalink]
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We can easily deduce here the general term of the sequence
$$a_{n+1}$$ = $$2 * {a_n}$$ - 3

We rewrite the formula for the forth and third term:
$$a_4$$ = $$2 * {a_3}$$ - 3

We resolve the equation for $$a_3$$.
$$a_3$$ = $$\frac{(a_4 +3)}{2} = \frac{22}{2}=11$$

Similarly, we calculate the preceding terms:
$$a_3$$ = $$2 * {a_2} - 3$$
$$a_2$$ = $$\frac{(a_3 +3)}{2} =\frac{14}{2}=7$$(not in the answer choices)

$$a_2$$ = $$2 * {a_1}- 3$$
$$a_1$$ = $$\frac{({a_2} +3)}{2} = \frac{10}{2}=5$$ (in the answer choices)

From here we notice that the terms are smaller and smaller.
The smallest term in the answer choices is 5, so we have to look at higher terms (higher than the one given, which is the $$a_4$$)

$$a_5$$ =$$2 * {a_4} - 3$$
$$a_5$$ =$$2*19 -3 = 35$$

Since we know that the fourth term is 19 and the fifth term is 35 there is no term in between, hence all the answers are:11, 5 and 35

Last edited by ElizabethCM on 03 Nov 2019, 04:24, edited 10 times in total. VP Joined: 20 Apr 2016
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Re: In a certain sequence of numbers, each term after the first. [#permalink]
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ElizabethCM wrote:
Below one solution using the sequence formula. I am sorry but I did not know how to edit the expressions here

Hi,
Plz be informed, you have to write it down. Attaching screenshot (for an answer) is not entertained.

I appreciate if you can read the RULES OF POSTING

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The above link will guide. Any doubt give a shout
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GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests Intern Joined: 19 Oct 2019
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Re: In a certain sequence of numbers, each term after the first. [#permalink]
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Thanks, Pranab, done, I just kept previewing but when we preview we do not see the final result formatted- sorry for so many edits !!! Re: In a certain sequence of numbers, each term after the first.   [#permalink] 03 Nov 2019, 04:25
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