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# 5 and 15 are the first two terms in a geometric sequence.

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Director
Joined: 29 Nov 2012
Posts: 749
5 and 15 are the first two terms in a geometric sequence.  [#permalink]

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22 Jun 2013, 04:47
3
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:45) correct 35% (01:44) wrong based on 196 sessions

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5 and 15 are the first two terms in a geometric sequence. What is the arithmetic difference between the 11th term and the 13th term?

A. 3*5^2
B. 5* 3^13 - 5 * 3^11
C. 5^13
D. 40 * 3^10
E. 3^12 - 3^10

Question regarding arithmetic difference is a - b / 2? or only a - b?
Manager
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Posts: 121
Location: India
Concentration: General Management, Technology
GMAT 1: 640 Q42 V37
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Re: 5 and 15 are the first two terms in a geometric sequence.  [#permalink]

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22 Jun 2013, 07:02
1
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fozzzy wrote:
5 and 15 are the first two terms in a geometric sequence. What is the arithmetic difference between the 11th term and the 13th term?

a 3*5^2
b 5* 3^13 - 5 * 3^11
c 5^13
d 40 * 3^10
e 3^12 - 3^10

Question regarding arithmetic difference is a - b / 2? or only a - b?

I think the answer choice should be 40 * 3^11. Please do check the source and correct me if I am wrong! Also, the fact that we are calculating the difference of the 13th and the 11th term since this is an increasing GP!

The first term or the a0 = 5 and a1 = 15. For geometric progression, a1 = r * a0 where r is the common term.
Hence, r comes out to be 3.

$$a13 - a11 = a0 * (r^13 - r^11) = 5 * (3^13 - 3^11) = 5 * 3^11 * (9-1) = 40 * 3^11$$

Hence, 40 * 3^11 should be the answer.

Regards,
Arpan
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Director
Joined: 29 Nov 2012
Posts: 749
Re: 5 and 15 are the first two terms in a geometric sequence.  [#permalink]

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22 Jun 2013, 07:07
1
The formula for GP is $$A1*[r ^{(n-1)}]$$

so for 11th term it will be 10 and for 13th term it will be 12

sequences-progressions-101891.html
Manager
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Re: 5 and 15 are the first two terms in a geometric sequence.  [#permalink]

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22 Jun 2013, 07:16
fozzzy wrote:
The formula for GP is $$A1*[r ^{(n-1)}]$$

so for 11th term it will be 10 and for 13th term it will be 12

sequences-progressions-101891.html

My apologies! Since I started of the series with a0 I completely screwed up the counting! As you have mentioned, the 13th term will have the 12th power and the 11th term will have the 10th power! *precisely the difference between choice [B] and [D]*

And as you have mentioned, the arithmetic difference is the the simple difference of the two terms leading to the answer [D]!

Regards,
Arpan
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Re: 5 and 15 are the first two terms in a geometric sequence.  [#permalink]

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22 Jun 2013, 07:22
fozzzy wrote:
5 and 15 are the first two terms in a geometric sequence. What is the arithmetic difference between the 11th term and the 13th term?

a 3*5^2
b 5* 3^13 - 5 * 3^11
c 5^13
d 40 * 3^10
e 3^12 - 3^10

Question regarding arithmetic difference is a - b / 2? or only a - b?

For a given Geometric Sequence, the $$n^{th}$$ term is $$t_n = a*r^{n-1}$$, where a is the first term and r is the common ratio. From the given problem, $$t_{11} = 5*3^{10}$$ and $$t_{13} = 5*3^{12}$$. Thus, the arithmetic difference is : $$5*3^{10}*(9-1)$$ = $$40*3^{10}$$.
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Posts: 52906
Re: 5 and 15 are the first two terms in a geometric sequence.  [#permalink]

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22 Jun 2013, 12:16
fozzzy wrote:
5 and 15 are the first two terms in a geometric sequence. What is the arithmetic difference between the 11th term and the 13th term?

A. 3*5^2
B. 5* 3^13 - 5 * 3^11
C. 5^13
D. 40 * 3^10
E. 3^12 - 3^10

Question regarding arithmetic difference is a - b / 2? or only a - b?

Similar questions to practice:
baker-s-dozen-128782-40.html#p1057517
if-the-sequence-x1-x2-x3-xn-is-such-that-x1-98536.html
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Re: 5 and 15 are the first two terms in a geometric sequence.  [#permalink]

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24 Jan 2016, 21:24
Answer comes out to be 5 * (3^13 - 3^11) = 5 * 3^11*(3^2 - 1) = 5 * 3^11 * 8 = 40 * 3^11....

Only B depicts correct answer; but OA is "D" which says answer is 40 * 3^10 ...which is wrong...

Am I right guys?
DS Forum Moderator
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Posts: 1431
Location: India
Re: 5 and 15 are the first two terms in a geometric sequence.  [#permalink]

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22 May 2017, 22:28
prathameshbhirud wrote:
Answer comes out to be 5 * (3^13 - 3^11) = 5 * 3^11*(3^2 - 1) = 5 * 3^11 * 8 = 40 * 3^11....

Only B depicts correct answer; but OA is "D" which says answer is 40 * 3^10 ...which is wrong...

Am I right guys?

Hi

You are taking 13th term as 5 * 3^13, NO, it should be 5 * 3^12

You are taking 11th term as 5 * 3^11, NO, it should be 5 * 3^10

Once you correct the values, you will get: 5 * 3^10 (3^2 - 1) = 5 * 3^10 * 8 = 40 * 3^10
Manager
Joined: 12 Sep 2017
Posts: 127
Re: 5 and 15 are the first two terms in a geometric sequence.  [#permalink]

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02 Feb 2019, 14:56
Hello everyone!

Can someone help me to find the common ratio here?

Kind regards!
Re: 5 and 15 are the first two terms in a geometric sequence.   [#permalink] 02 Feb 2019, 14:56
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