What is the difference between the sixth and the fifth terms

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

What is the difference between the sixth and the fifth terms

by BTGmoderatorDC » Wed Sep 18, 2019 8:19 pm

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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

OA E

Source: Official Guide

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Source: Beat The GMAT — Problem Solving | Wed Sep 18, 2019 8:19 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Thu Sep 19, 2019 10:44 pm

BTGmoderatorDC 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

OA E

Source: Official Guide

Given that the nth term = n + 2^(n - 1), the 6th term = 6 + 2^(6 - 1) = 6 + 2^5 = 38. And the 5th term = 5 + 2^(5 - 1) = 5 + 2^4 = 21

Thus, the difference between the sixth and the fifth terms of the sequence = 38 - 21 = 17

The correct answer: E

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Sep 24, 2019 10:23 am

BTGmoderatorDC 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

OA E

Source: Official Guide

To find the sixth term, let's first substitute 6 for n.

6 + 2^(6-1)6 + 2^5

6 + 32 = 38

To find the fifth term, we substitute 5 for n.

5 + 2^(5-1)

5 + 2^4

5 + 16 = 21

The difference between the 6th and 5th terms of the sequence is 38 - 21 = 17.

Answer: E

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