In a certain sequence term_1 = 64

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by Brent@GMATPrepNow » Wed Jun 13, 2018 6:24 am

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In a certain sequence, term1 = 64, and for all n > 1, termn = (2^n)(termn-1)
What is the value of term11/term8 ?

A) 2^3
B) 2^6
C) 2^9
D) 2^27
E) 2^30

Answer: E
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Source: Beat The GMAT — Problem Solving | Wed Jun 13, 2018 6:24 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

In a certain sequence term_1 = 64

by Brent@GMATPrepNow » Fri Jun 15, 2018 8:23 am

Brent@GMATPrepNow wrote:In a certain sequence, term1 = 64, and for all n > 1, termn = (2^n)(termn-1)
What is the value of term11/term8 ?

A) 2^3
B) 2^6
C) 2^9
D) 2^27
E) 2^30

Let's list a few terms and look for a pattern

term1 = 64 = 2^8
term2 = (2^8)(2^2)
term3 = (2^8)(2^2)(2^3)
term4 = (2^8)(2^2)(2^3)(2^4)
.
.
.
term8 = (2^8)(2^2)(2^3)(2^4)(2^5)(2^6)(2^7)(2^8)
.
.
.
term11 = (2^8)(2^2)(2^3)(2^4)(2^5)(2^6)(2^7)(2^8)(2^9)(2^10)(2^11)

So, term11/term8 = (2^8)(2^2)(2^3)(2^4)(2^5)(2^6)(2^7)(2^8)(2^9)(2^10)(2^11)/(2^8)(2^2)(2^3)(2^4)(2^5)(2^6)(2^7)(2^8)
= (2^9)(2^10)(2^11)
= 2^30

Answer: E

Cheers,
Brent

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