In the sequence s1, s2, s3,....,sn each term after the first is one more than twice the previous term. If s1=3 then what is the value of (s21-s20) ?
A) 2^19
B) 2^20
C) 2^21
D) (2^20) - 1
E) (2^20) + 1
Target Test Prep is 20% off right now!
Use code FLASH20
Available with Beat the GMAT members only code
MORE DETAILS
Series & Sequences
This topic has expert replies
-
[email protected]
- Newbie | Next Rank: 10 Posts
- Posts: 3
- Joined: Mon Apr 30, 2012 9:18 am
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let's list a few terms of the sequence to get a feel for the pattern:[email protected] wrote:In the sequence s1, s2, s3,....,sn each term after the first is one more than twice the previous term. If s1=3 then what is the value of (s21-s20) ?
A) 2^19
B) 2^20
C) 2^21
D) (2^20) - 1
E) (2^20) + 1
s1 = 3
s2 = (2)(3) + 1 = 7
s3 = (2)(7) + 1 = 15
s4 = (2)(15) + 1 = 31
s5 = (2)(31) + 1 = 63
See the pattern yet? Here it is:
s1 = 3 = (2^2) - 1
s2 = (2)(3) + 1 = 7 = (2^3) - 1
s3 = (2)(7) + 1 = 15 = (2^4) - 1
s4 = (2)(15) + 1 = 31 = (2^5) - 1
s5 = (2)(31) + 1 = 63 = (2^6) - 1
.
.
.
.
s20 = (2^21) - 1
s21 = (2^22) - 1
So, s21 - s20 = (2^22) - 1 - (2^21) - 1
= (2^22) - (2^21)
= (2^21)(2^1 - 1)
= (2^21)(2 - 1)
= (2^21)(1)
= C
Here's a free video on sequences: https://www.gmatprepnow.com/module/gmat- ... /video/923
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
==> S_1=3=(2^2)-1 (Because twice --> 2^n)
S_2=1+2S_1=1+2*3=7=(2^3)-1
S_3=1+2S_2=1+2*7=15=(2^4)-1..........................
S_21=(2^22)-1 and S_20=(2^21)-1,
then S_21-S-20=(2^22)-1-[(2^21)-1]=(2^22)-1-(2^21)-1=(2^22)-(2^21)=(2-1)(2^21)=1*2^21=2^21.
Therefore the best answer is C
www.mathrevolution.com
- The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.
- The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.
- The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare
- Hitting a score of 45 is very easy and points and 49-51 is also doable.
- Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson
- Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8
==> S_1=3=(2^2)-1 (Because twice --> 2^n)
S_2=1+2S_1=1+2*3=7=(2^3)-1
S_3=1+2S_2=1+2*7=15=(2^4)-1..........................
S_21=(2^22)-1 and S_20=(2^21)-1,
then S_21-S-20=(2^22)-1-[(2^21)-1]=(2^22)-1-(2^21)-1=(2^22)-(2^21)=(2-1)(2^21)=1*2^21=2^21.
Therefore the best answer is C
www.mathrevolution.com
- The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.
- The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.
- The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare
- Hitting a score of 45 is very easy and points and 49-51 is also doable.
- Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson
- Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8
