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## In the sequence 1, 2, 4, 8, 16, 32, â€¦,

tagged by: VJesus12

This topic has 3 expert replies and 1 member reply

### Top Member

VJesus12 Master | Next Rank: 500 Posts
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#### In the sequence 1, 2, 4, 8, 16, 32, â€¦,

Fri Dec 15, 2017 6:55 am
In the sequence 1, 2, 4, 8, 16, 32, â€¦, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?
$$A.\ \ \ 2^{18}$$ $$B.\ \ \ 3\left(2\right)^{^{17}}$$ $$\left(C.\ \ \ 7(2\right)^{16}$$ $$D.3\left(2\right)^{16}$$ $$E.7\left(2\right)^{15}$$

The OA is E.

What is the formula that I should use here? Experts, can you show me how to solve this PS question? Thanks in advanced.

### GMAT/MBA Expert

EconomistGMATTutor GMAT Instructor
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Fri Dec 15, 2017 8:15 am
Hello VJesus12.

Let's take a look at your question.

We can rewrite the sequence as follows: $$2^0\ \ ,\ \ \ 2^1\ ,\ \ 2^2\ ,\ 2^3\ ,\ \ 2^4\ ,\ \ \ 2^5\ ,\ \ \ 2^6\ ,\ \dots$$ This is equivalent to say that the nth term is $$a_n=2^{n-1}.$$ So, we have that $$a_{16}=2^{15},\ \ a_{17}=2^{16}\ \ \ and\ a_{18}=2^{17}.$$ Therefore $$a_{16}+a_{17}+a_{18}=2^{15}+2^{16}+2^{17}=2^{15}\left(1+2+2^2\right)=7\left(2\right)^{15}.$$ So, the correct answer is E.

Feel free to ask me again if you have a doubt.

Regards.

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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Fri Dec 15, 2017 8:07 am
VJesus12 wrote:
In the sequence 1, 2, 4, 8, 16, 32, â€¦, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?
$$A.\ \ \ 2^{18}$$ $$B.\ \ \ 3\left(2\right)^{^{17}}$$ $$\left(C.\ \ \ 7(2\right)^{16}$$ $$D.3\left(2\right)^{16}$$ $$E.7\left(2\right)^{15}$$
First notice the PATTERN:
term_1 = 1 (aka 2^0)
term_2 = 2 (aka 2^1)
term_3 = 4 (aka 2^2)
term_4 = 8 (aka 2^3)
term_5 = 16 (aka 2^4)
.
.
.
Notice that the exponent is 1 LESS THAN the term number.

So, term_16 = 2^15
term_17 = 2^16
term_18 = 2^17

We want to find the sum 2^15 + 2^16 + 2^17
We can do some factoring: 2^15 + 2^16 + 2^17 = 2^15(1 + 2^1 + 2^2)
= 2^15(1 + 2 + 4)
= 2^15(7)
= E

Cheers,
Brent

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GMATWisdom Master | Next Rank: 500 Posts
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Fri Dec 15, 2017 8:00 am
VJesus12 wrote:
In the sequence 1, 2, 4, 8, 16, 32, â€¦, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?
$$A.\ \ \ 2^{18}$$ $$B.\ \ \ 3\left(2\right)^{^{17}}$$ $$\left(C.\ \ \ 7(2\right)^{16}$$ $$D.3\left(2\right)^{16}$$ $$E.7\left(2\right)^{15}$$

The OA is E.

What is the formula that I should use here? Experts, can you show me how to solve this PS question? Thanks in advanced.
the series is 1,2,4,8,16,32,............

in terms of power of 2 we can rewrite it in the form

2^0,2^1,2^2,2^3,2^4,2^5,........

=> nth term = 2^(n-1)

therefore 16th, 17th ,and 18th term would be 2^15,2^16,and 2^17

and their sum = 2^15+2^16+2^17= 2^15 * (1+2+4) = 7(2^15)

hence option E is correct

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11408 messages
Followed by:
1229 members
5254
GMAT Score:
770
Fri Dec 15, 2017 8:07 am
VJesus12 wrote:
In the sequence 1, 2, 4, 8, 16, 32, â€¦, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?
$$A.\ \ \ 2^{18}$$ $$B.\ \ \ 3\left(2\right)^{^{17}}$$ $$\left(C.\ \ \ 7(2\right)^{16}$$ $$D.3\left(2\right)^{16}$$ $$E.7\left(2\right)^{15}$$
First notice the PATTERN:
term_1 = 1 (aka 2^0)
term_2 = 2 (aka 2^1)
term_3 = 4 (aka 2^2)
term_4 = 8 (aka 2^3)
term_5 = 16 (aka 2^4)
.
.
.
Notice that the exponent is 1 LESS THAN the term number.

So, term_16 = 2^15
term_17 = 2^16
term_18 = 2^17

We want to find the sum 2^15 + 2^16 + 2^17
We can do some factoring: 2^15 + 2^16 + 2^17 = 2^15(1 + 2^1 + 2^2)
= 2^15(1 + 2 + 4)
= 2^15(7)
= E

Cheers,
Brent

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!

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