In a certain sequence, termn = 2(termn-1)^n
If term6/term5 = 4^8, what is the value of term4 ?
A) 2^(0.4)
B) 2^(0.5)
C) 2^(0.75)
D) 2^(0.8)
E) 2^(1.25)
Answer: A
Source: www.gmatprepnow.com
Difficulty level: 700+
Tricky sqeuence Q: In a certain sequence, termn = 2(tn-1)^n
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term6 = 2(term5)^6 ----- equation (1)
Replace term6 in equation (1)
2(term5)^6 / term5 = 4^8
Note 4^8 = 2^16
2(term5)^6 / term5 = 2^16
Divide both sides by 2
(term5^6)/term5 = 2^15
Therefore; term5^5 = 2^15 ----- 1
term5 = 2(term4)^5
Substitute term5 in our equation (2)
[2(term4^5)]^5 = 2^15
2^5(term4^25) = 2^15
Divide both sides by 2^5
term4^25 = 2^10
Find the 25th root of both sides
term4 = 2^(10/25)
term4 = 2^(0.4)
Replace term6 in equation (1)
2(term5)^6 / term5 = 4^8
Note 4^8 = 2^16
2(term5)^6 / term5 = 2^16
Divide both sides by 2
(term5^6)/term5 = 2^15
Therefore; term5^5 = 2^15 ----- 1
term5 = 2(term4)^5
Substitute term5 in our equation (2)
[2(term4^5)]^5 = 2^15
2^5(term4^25) = 2^15
Divide both sides by 2^5
term4^25 = 2^10
Find the 25th root of both sides
term4 = 2^(10/25)
term4 = 2^(0.4)
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- Brent@GMATPrepNow
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Let k = term 4 [this will make our calculations much easier to follow]Brent@GMATPrepNow wrote:In a certain sequence, termn = 2(termn-1)^n
If term6/term5 = 4^8, what is the value of term4 ?
A) 2^(0.4)
B) 2^(0.5)
C) 2^(0.75)
D) 2^(0.8)
E) 2^(1.25)
Answer: A
Source: www.gmatprepnow.com
Difficulty level: 700+
term5 = 2(term4)^5
= 2k^5
term6 = 2(term5)^6
= 2(2k^5)^6
= (2)(2^6)(k^30)
= (2^7)(k^30)
So, (term6)/(term5) = [(2^7)(k^30)]/(2k^5)
= (2^6)(k^25)
Since we're told that (term6)/(term5) = 4^8, we can write the following...
(2^6)(k^25) = 4^8
(2^6)(k^25) = (2^2)^8
(2^6)(k^25) = 2^16
Divide both sides by 2^6 to get: k^25 = 2^10
Raise both sides to the power of 1/25 to get: (k^25)^(1/25) = (2^10)^(1/25)
Simplify: k = 2^(10/25)
Rewrite as: k = 2^(0.4) = term 4
Answer: A
Cheers,
Brent