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

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5 and 15 are the first two terms in a geometric sequence. [#permalink] New post 22 Jun 2013, 04:47
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Question Stats:

64% (01:57) correct 36% (00:54) wrong based on 64 sessions
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

[Reveal] Spoiler:
Question regarding arithmetic difference is a - b / 2? or only a - b?
[Reveal] Spoiler: OA

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Re: 5 and 15 are the first two terms in a geometric sequence. [#permalink] New post 22 Jun 2013, 07:02
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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

[Reveal] Spoiler:
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.

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Arpan
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Re: 5 and 15 are the first two terms in a geometric sequence. [#permalink] New post 22 Jun 2013, 07:07
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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
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Re: 5 and 15 are the first two terms in a geometric sequence. [#permalink] New post 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]!

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Re: 5 and 15 are the first two terms in a geometric sequence. [#permalink] New post 22 Jun 2013, 07:22
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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

[Reveal] Spoiler:
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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Re: 5 and 15 are the first two terms in a geometric sequence. [#permalink] New post 22 Jun 2013, 12:16
Expert's post
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

[Reveal] Spoiler:
Question regarding arithmetic difference is a - b / 2? or only a - b?


Similar questions to practice:
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Re: 5 and 15 are the first two terms in a geometric sequence.   [#permalink] 22 Jun 2013, 12:16
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5 and 15 are the first two terms in a geometric sequence.

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