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Manager  Joined: 02 Dec 2012
Posts: 173
What is the difference between the sixth and the fifth terms  [#permalink]

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2
15 00:00

Difficulty:   5% (low)

Question Stats: 84% (01:25) correct 16% (01:30) wrong based on 1560 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: 59726
Re: What is the difference between the sixth and the fifth terms  [#permalink]

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3
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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Manager  G
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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
Manager  Joined: 10 Aug 2009
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Concentration: Entrepreneurship, Strategy
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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: 59726
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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Target Test Prep Representative V
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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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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
Senior Manager  P
Joined: 12 Dec 2015
Posts: 447
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--> correct

Analysis: t6-t5 = 6 + 2^5 - 5 -2^4=1+2^4=17
Intern  B
Joined: 28 Jan 2019
Posts: 37
Re: What is the difference between the sixth and the fifth terms  [#permalink]

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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 Re: What is the difference between the sixth and the fifth terms   [#permalink] 26 Nov 2019, 09:23
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