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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
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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
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Re: In a certain sequence of numbers, each term after the first. [#permalink]
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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

Originally posted by ElizabethCM on 03 Nov 2019, 02:50.
Last edited by ElizabethCM on 03 Nov 2019, 04:24, edited 10 times in total.
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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

RULES TO POST

The above link will guide. Any doubt give a shout
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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 !!!
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Re: In a certain sequence of numbers, each term after the first. [#permalink]
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Re: In a certain sequence of numbers, each term after the first. [#permalink]
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