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In a certain sequence of numbers, each term after the first.
[#permalink]
02 Jan 2016, 00:38

Question Stats:

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

Answer:

A.5

B.8

C.11

D.16

E.22

F.35

Answer:

Show: ::

a,c,f

Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4804**

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Re: In a certain sequence of numbers, each term after the first.
[#permalink]
02 Jan 2016, 18:16

1

Expert Reply

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

The answer is a,c,f

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

A.5

B.8

C.11

D.16

E.22

F.35

The answer is a,c,f

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?

_________________

Sandy

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Re: In a certain sequence of numbers, each term after the first.
[#permalink]
03 Sep 2018, 15:50

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.

so answer is a,c,f

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.

so answer is a,c,f

Re: In a certain sequence of numbers, each term after the first.
[#permalink]
14 Feb 2019, 02:07

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

Re: In a certain sequence of numbers, each term after the first.
[#permalink]
02 Oct 2019, 08:59

2

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

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

Re: In a certain sequence of numbers, each term after the first.
[#permalink]
Updated on: 03 Nov 2019, 04:24

1

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

\(a_{n+1}\) = \(2 * {a_n}\) - 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.

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

Re: In a certain sequence of numbers, each term after the first.
[#permalink]
03 Nov 2019, 03:30

1

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]
03 Nov 2019, 04:25

1

Thanks, Pranab, done, I just kept previewing but when we preview we do not see the final result formatted- sorry for so many edits !!!

gmatclubot

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