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What is the difference between the sixth and the fifth terms

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Walkabout
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What is the difference between the sixth and the fifth terms [#permalink] New post   20 Dec 2012, 09:02
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What is the difference between the sixth and the fifth terms of the sequence 2, 4, 7, ... whose nth term is n + 2^(n - 1)?

(A) 2
(B) 3
(C) 6
(D) 16
(E) 17
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E
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Bunuel
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Re: What is the difference between the sixth and the fifth terms [#permalink] New post   20 Dec 2012, 09:04
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Walkabout wrote:
What is the difference between the sixth and the fifth terms of the sequence 2, 4, 7, ... whose nth term is n + 2^(n - 1)?

(A) 2
(B) 3
(C) 6
(D) 16
(E) 17


Given that \(a_n=n+2^{n-1}\), thus:

\(a_6=6+2^{6-1}=38\);
\(a_5=5+2^{5-1}=21\);

The difference is 38-21=17.

Answer: E.
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Re: What is the difference between the sixth and the fifth terms [#permalink] New post   25 Nov 2014, 14:02
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Bunuel wrote:
Walkabout wrote:
What is the difference between the sixth and the fifth terms of the sequence 2, 4, 7, ... whose nth term is n + 2^(n - 1)?

(A) 2
(B) 3
(C) 6
(D) 16
(E) 17


Given that \(a_n=n+2^{n-1}\), thus:

\(a_6=6+2^{6-1}=38\);
\(a_5=5+2^{5-1}=21\);

The difference is 38-21=17.

Answer: E.


Just one question, why do they mention 2, 4, 7. Is that to throw a test-taker off?
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Re: What is the difference between the sixth and the fifth terms [#permalink] New post   26 Nov 2014, 05:10
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Bigred2008 wrote:
Bunuel wrote:
Walkabout wrote:
What is the difference between the sixth and the fifth terms of the sequence 2, 4, 7, ... whose nth term is n + 2^(n - 1)?

(A) 2
(B) 3
(C) 6
(D) 16
(E) 17


Given that \(a_n=n+2^{n-1}\), thus:

\(a_6=6+2^{6-1}=38\);
\(a_5=5+2^{5-1}=21\);

The difference is 38-21=17.

Answer: E.


Just one question, why do they mention 2, 4, 7. Is that to throw a test-taker off?


2, 4, and 7, are the first, second and the third terms of the sequence whose nth term is n + 2^(n - 1). For n = 1, n + 2^(n - 1) = 1 + 2^0 = 2, for n = 2, n + 2^(n - 1) = 2 + 2^1 = 4, and for n = 3, n + 2^(n - 1) = 3 + 2^2 = 7. So, those numbers are given simply as an example.
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Re: What is the difference between the sixth and the fifth terms [#permalink] New post   13 Jul 2016, 07:30
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Walkabout wrote:
What is the difference between the sixth and the fifth terms of the sequence 2, 4, 7, ... whose nth term is n + 2^(n - 1)?

(A) 2
(B) 3
(C) 6
(D) 16
(E) 17


For the sixth term, we need to substitute 6 for n, and for the fifth term, we need to substitute 5 for n. Then we'll find the difference between the two terms.

Let’s first plug 6 in for n.

6 + 2^(6-1)

6 + 2^5

6 + 32 = 38

Next let’s plug 5 in for n.

5 + 2^(5-1)

5 + 2^4

5 + 16 = 21

Thus, the difference between the 6th and 5th term of the sequence is 38 – 21 = 17.

Answer is E.
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Re: What is the difference between the sixth and the fifth terms [#permalink] New post   31 Jan 2017, 17:37
Plug in 6 and 5 for the sixth and fifth sequence respectively.....

Sixth sequence = 6 + 2^(6-1) = 38

Fifth sequence = 5 + 2^(5-1) = 21

38-21
=
17
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Re: What is the difference between the sixth and the fifth terms [#permalink] New post   29 Jun 2017, 19:28
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Notice that 2 raised to any positive number will aways be even.

Hence the sixth term will be even+even = even
The fifth term will be odd+even = odd

The only two answers that are odd are B and E. I would say that looking at the sequence we can say that the gap is expanding, hence answer is E
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Re: What is the difference between the sixth and the fifth terms [#permalink] New post   22 Oct 2019, 07:27
What is the difference between the sixth and the fifth terms of the sequence 2, 4, 7, ... whose nth term is n + 2^(n - 1)?

(A) 2
(B) 3
(C) 6
(D) 16
(E) 17--> correct

Analysis: t6-t5 = 6 + 2^5 - 5 -2^4=1+2^4=17
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Re: What is the difference between the sixth and the fifth terms [#permalink] New post   26 Nov 2019, 09:23
n6 = 6+2^5
n5 = 5+2^4

n6-n5= 6+2^5-(5+2^4)
=1+2^5-2^4
=1+2^4(2-1)
=1+16(1)
=17
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What is the difference between the sixth and the fifth terms [#permalink] New post   10 Jan 2021, 07:53
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Walkabout wrote:
What is the difference between the sixth and the fifth terms of the sequence 2, 4, 7, ... whose nth term is n + 2^(n - 1)?

(A) 2
(B) 3
(C) 6
(D) 16
(E) 17


AS, \(a_n=n+2^{n-1}\)

\(∴ a_6=6+2^{6-1}=38\);
\(∴ a_5=5+2^{5-1}=21\);

The difference \(=38-21=17\)

The answer is \(E\)
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Re: What is the difference between the sixth and the fifth terms [#permalink] New post   23 Feb 2021, 17:31
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Re: What is the difference between the sixth and the fifth terms [#permalink] New post   28 May 2023, 07:22
To find the difference between the sixth and fifth terms of the given sequence, we need to calculate these terms using the provided formula.

The formula for the nth term of the sequence is given as n + 2^(n - 1).

Let's calculate the fifth term:
n = 5
5 + 2^(5 - 1) = 5 + 2^4 = 5 + 16 = 21

Now, let's calculate the sixth term:
n = 6
6 + 2^(6 - 1) = 6 + 2^5 = 6 + 32 = 38

The difference between the sixth and fifth terms is:
38 - 21 = 17

Therefore, the difference between the sixth and fifth terms of the sequence is 17.

The correct answer is (E) 17.
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Re: What is the difference between the sixth and the fifth terms [#permalink]
28 May 2023, 07:22
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