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Tricky sqeuence Q: In a certain sequence, termn = 2(tn-1)^n

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Tricky sqeuence Q: In a certain sequence, termn = 2(tn-1)^n

by Brent@GMATPrepNow » Tue Apr 04, 2017 7:48 am
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

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by [email protected] » Tue Apr 04, 2017 8:09 am
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)
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by Brent@GMATPrepNow » Wed Apr 05, 2017 6:33 am
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+
Let k = term 4 [this will make our calculations much easier to follow]

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
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