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OG PS #171 - Easy Sequence Question!

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OG PS #171 - Easy Sequence Question!

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Hello all,

I've never posted before, but I have a simple question about OG PS question #171. Question is:

"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."

According to the answer, you simply plug 6 and 5 into the term formula, but my question is why did they list seemingly random numbers first... I had assumed that those were the 1st, 2nd, and 3rd terms, I tried to plug them in as recursive numbers.

If someone could explain that would be fantastic Smile

Thanks guys! Happy studying and/or happy tutoring!

Kali

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kalifalk wrote:
Hello all,

I've never posted before, but I have a simple question about OG PS question #171. Question is:

"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."

According to the answer, you simply plug 6 and 5 into the term formula, but my question is why did they list seemingly random numbers first... I had assumed that those were the 1st, 2nd, and 3rd terms, I tried to plug them in as recursive numbers.

If someone could explain that would be fantastic Smile

Thanks guys! Happy studying and/or happy tutoring!

Kali
numbers are not random. plug in them to the formula n+2^n-1

so, ur 1st term will be equal to 1+2^1-1=1+1=2 (as it is mentioned in ur sequence)
ur 2nd term is 2+2^2-12+2=4
ur 3d term is 3+2^3-1=3+4=7

the same sequence (2, 4, 7....) is listed in the q.stem

hope it helps

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Thanks Buddy

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kalifalk wrote:
Hello all,

I've never posted before, but I have a simple question about OG PS question #171. Question is:

"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."

According to the answer, you simply plug 6 and 5 into the term formula, but my question is why did they list seemingly random numbers first... I had assumed that those were the 1st, 2nd, and 3rd terms, I tried to plug them in as recursive numbers.

If someone could explain that would be fantastic Smile

Thanks guys! Happy studying and/or happy tutoring!

Kali
The first term in the sequnce is n=0. So for the 5th term, n=4 and 6th term , n=5.
Thus your answer comes to (4+2)^(4-1) which 6^3 and the 6th term should be (5+2)^(5-1) which is 7^4.

Here, as you notice value of n is 1 less than the term of the sequnce (Eg: Sixth term is n=5). I feel this is the trick that they are testing.

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kalifalk wrote:
Hello all,

I've never posted before, but I have a simple question about OG PS question #171. Question is:

"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."

According to the answer, you simply plug 6 and 5 into the term formula, but my question is why did they list seemingly random numbers first... I had assumed that those were the 1st, 2nd, and 3rd terms, I tried to plug them in as recursive numbers.

If someone could explain that would be fantastic Smile

Thanks guys! Happy studying and/or happy tutoring!

Kali
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

Solution:

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

_________________
Jeffrey Miller Head of GMAT Instruction

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Hi All,

We're told that a sequence 2, 4, 7... is defined by the following: the Nth term is N + 2^(N - 1). We're asked for the the difference between the sixth and the fifth terms of the sequence.

While sequence questions can sometimes look complex, they generally involve basic Arithmetic rules, so it can often help to figure out the first few terms of the sequence (so you understand how the sequence "works").

Here, the Nth term in the sequence can be determined with... N + 2^(N - 1)

1st term --> N = 1..... 1 + 2^(0) = 1+1 = 2
2nd term --> N = 2..... 2 + 2^(1) = 2+2 = 4
3rd term --> N = 3..... 3 + 2^(2) = 3+4 = 7
Etc.

We're asked for the difference between the 6th and 5th terms...
5th term --> N = 5..... 5 + 2^(4) = 5+16 = 21
6th term --> N = 6..... 6 + 2^(5) = 6+32 = 38
38 - 21 = 17

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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