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In a certain sequence, termn = 2(tn-1)^n

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In a certain sequence, termn = 2(tn-1)^n  [#permalink]

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New post 04 Apr 2017, 08:45
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63% (02:59) correct 37% (03:02) wrong based on 121 sessions

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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) \(2^{1.25}\)

*kudos for all correct solutions

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Re: In a certain sequence, termn = 2(tn-1)^n  [#permalink]

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New post 04 Apr 2017, 09:04
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(term6)/(term5) = 4^8, can be written as

[2 * (term5)^6]/[2 * (term4)^5] = 2^16, this can be further simplified to

[(2* (term4)^5)^6]/[(term4)^5] = 2^16, this can be further simplified to

[(2^6) * (term4^30)] /[(term4)^5] = 2^16, this can be further simplified to

term4^25 = 2^10 ==> term4 = 2 ^ (10/25) ==> term4 = 2^0.4

Answer is A) 2^0.4
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In a certain sequence, termn = 2(tn-1)^n  [#permalink]

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New post 04 Apr 2017, 09:27
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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) \(2^{1.25}\)

*kudos for all correct solutions


termn = 2(termn-1)\(^n\)

term6 = 2(term5)\(^6\) = \(4^8\) * (term5) --- (given : (term6)/(term5) = \(4^8\) )

(term5)\(^5\) = \((2^2)^8\)/2 = \(2^{15}\)

(term5) = \(2^3\)

now term5 = 2(term4)\(^5\)

2(term4)\(^5\) = \(2^3\)

(term4)\(^5\) = \(2^2\)

(term4) = \(2^{2/5}\) = \(2^{0.4}\)

Hence option A is correct
Hit Kudos if you liked it 8-)
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Re: In a certain sequence, termn = 2(tn-1)^n  [#permalink]

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New post 05 Apr 2017, 07:27
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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) \(2^{1.25}\)


Let k = term4 [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) = \(\frac{(2^7)(k^{30})}{(2k^5)}\)
= \(2^6k^{25}\)

Since we're told that (term6)/(term5) = \(4^8\), we can write the following...
\(2^6k^{25} = 4^8\)

\(2^6k^{25} = (2^2)\)\(^8\)

\(2^6k^{25} = 2^{16}\)

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: \(k = 2^{10/25}\)

Simplify: \(k = 2^{0.4}\)

Answer: A

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Re: In a certain sequence, termn = 2(tn-1)^n  [#permalink]

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New post 20 Aug 2018, 18:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a certain sequence, termn = 2(tn-1)^n &nbs [#permalink] 20 Aug 2018, 18:10
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