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

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CEO
Joined: 12 Sep 2015
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In a certain sequence, termn = 2(tn-1)^n  [#permalink]

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04 Apr 2017, 08:45
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75% (hard)

Question Stats:

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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04 Apr 2017, 09:04
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1
(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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04 Apr 2017, 09:27
1
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
CEO
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Re: In a certain sequence, termn = 2(tn-1)^n  [#permalink]

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05 Apr 2017, 07:27
1
Top Contributor
2
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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20 Aug 2018, 18:10
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# In a certain sequence, termn = 2(tn-1)^n

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