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Re: What is the difference between the sixth and the fifth terms [#permalink]

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24 Aug 2014, 12:52

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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

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.
_________________

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.
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: What is the difference between the sixth and the fifth terms [#permalink]

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29 Jun 2017, 19:28

1

This post received KUDOS

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 _________________

Kudosity killed the cat but your kudos can save it.