BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Different values thru the geometric progression?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Fri Dec 17, 2010 5:28 pm
ov25 wrote:For the geometric sequence, a1, a1*d, a1*d^2, ... a1*d^n, the sum of the first three terms is
21, what is the sum of the first 6 terms?
(1) a1=3
(2) d>0

discuss
a1*d(1+d)+a1=21, to find the sum of the first six we need to find d
st(1) a1=3 <=> 3*d(1+d) +3=21 <=> 3d+3*d^2=18 <=> d^2+d-6=0 <=> (d+3)(d-2)=0 => 2 answers for d {-3:2} Not sufficient
st(2) d>0. Not sufficient.

Combining st(1&2) d=2 Sufficient.

IOM C
Top
Senior | Next Rank: 100 Posts
Posts: 70
Joined: Sun Jul 22, 2007 11:43 pm
Thanked: 8 times

by Bharat » Fri Dec 17, 2010 5:38 pm
Answer: C (both together are sufficient).

as per given condition: a + ad + ad^2 = 21 (=S3)
a*(1 + d + d^2) = 21
Hence To calculate the sum of 6 terms, we need to know both a & d.
lets check the given conditions:

I: a = 3: it means: (1+ d+ d^2) = 7
solve to get: (d+3)(d-2) = 0 -> d = -3, 2 NOT SUFFICIENT.

II: d > 0: NOT SUFFICENT (value of a is still wide open)

Take I & II together: d = 2, a = 3 SUFFICIENT. Hence (D)

Let me know if you have questions.
Regards,
Bharat.
Top
Post new topic Post Reply
• Page 1 of 1