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Manager  Joined: 02 Dec 2012
Posts: 174
What is the difference between the sixth and the fifth terms  [#permalink]

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Difficulty:   5% (low)

Question Stats: 83% (01:27) correct 17% (01:33) wrong based on 1725 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 55709
Re: What is the difference between the sixth and the fifth terms  [#permalink]

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1
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.

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Concentration: Entrepreneurship, Strategy
Schools: Darden '17 (M\$)
Re: What is the difference between the sixth and the fifth terms  [#permalink]

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Bunuel 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.

Just one question, why do they mention 2, 4, 7. Is that to throw a test-taker off?
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Math Expert V
Joined: 02 Sep 2009
Posts: 55709
Re: What is the difference between the sixth and the fifth terms  [#permalink]

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Bigred2008 wrote:
Bunuel 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.

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]

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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

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.

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Joined: 24 Sep 2016
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Location: United States (CT)
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Re: What is the difference between the sixth and the fifth terms  [#permalink]

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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
Manager  S
Joined: 22 Nov 2016
Posts: 205
Location: United States
GPA: 3.4
Re: What is the difference between the sixth and the fifth terms  [#permalink]

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1
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]

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_________________ Re: What is the difference between the sixth and the fifth terms   [#permalink] 26 Jul 2018, 09:40
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