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 Author: Bunuel [ 02 Jul 2021, 05:45 ] Post subject: In a certain sequence, the term an is defined as the value of x that In a certain sequence, the term $$a_n$$ is defined as the value of x that satisfies the equation $$2 = \frac{x}{2} -a_{n- 1}$$. If $$a_6 =156$$, what is the value of $$a_2$$?(A) 1(B) 6(C) 16(D) 26(E) 106

 Author: chetan2u [ 03 Jul 2021, 22:31 ] Post subject: In a certain sequence, the term an is defined as the value of x that Bunuel wrote:In a certain sequence, the term $$a_n$$ is defined as the value of x that satisfies the equation $$2 = \frac{x}{2} -a_{n- 1}$$. If $$a_6 =156$$, what is the value of $$a_2$$?(A) 1(B) 6(C) 16(D) 26(E) 106$$2 = \frac{x}{2} -a_{n- 1}$$$$\frac{x}{2} =2+a_{n- 1}$$$$x=a_n=4+2a_{n-1}$$, as x is nothing but $$a_n$$. Two ways I. Find the lower terms from the given value$$a_n=4+2*a_{n-1}$$$$a_6=4+2*a_{5}$$$$156=4+2*a_5……..a_5=76$$$$a_5=4+2*a_{4}$$$$76=4+2*a_4……..a_4=36$$$$a_4=4+2*a_{3}$$$$36=4+2*a_3……..a_3=16$$$$a_3=4+2*a_{2}$$$$16=4+2*a_2……..a_2=6$$II. Use options. A. 1…. $$a_3=4+2*a_{2}=4+2=6……… a_4=4+2*a_{3}=4+12=16……….. a_5=4+2*a_{4}$$$$=4+32=36……….. a_6=4+2*a_{5}=4+72=76\neq 156$$B. 6…. $$a_3=4+2*a_{2}=4+12=16……… a_4=4+2*a_{3}=4+32=36……….. a_5=4+2*a_{4}$$$$=4+72=76……….. a_6=4+2*a_{5}=4+76=156$$…..CorrectB

 Author: axbycz37 [ 11 Jul 2021, 04:42 ] Post subject: In a certain sequence, the term an is defined as the value of x that chetan2u wrote:Bunuel wrote:In a certain sequence, the term $$a_n$$ is defined as the value of x that satisfies the equation $$2 = \frac{x}{2} -a_{n- 1}$$. If $$a_6 =156$$, what is the value of $$a_2$$?(A) 1(B) 6(C) 16(D) 26(E) 106$$2 = \frac{x}{2} -a_{n- 1}$$$$\frac{x}{2} =2+a_{n- 1}$$$$x=a_n=2+a_{n-1}$$, as x is nothing but $$a_n$$. Two ways I. Find the lower terms from the given value$$a_n=4+2*a_{n-1}$$$$a_6=4+2*a_{5}$$$$156=4+2*a_5……..a_5=76$$$$a_5=4+2*a_{4}$$$$76=4+2*a_4……..a_4=36$$$$a_4=4+2*a_{3}$$$$36=4+2*a_3……..a_3=16$$$$a_3=4+2*a_{2}$$$$16=4+2*a_2……..a_2=6$$II. Use options. A. 1…. $$a_3=4+2*a_{2}=4+2=6……… a_4=4+2*a_{3}=4+12=16……….. a_5=4+2*a_{4}$$$$=4+32=36……….. a_6=4+2*a_{5}=4+72=76\neq 156$$B. 6…. $$a_3=4+2*a_{2}=4+12=16……… a_4=4+2*a_{3}=4+32=36……….. a_5=4+2*a_{4}$$$$=4+72=76……….. a_6=4+2*a_{5}=4+76=156$$…..CorrectBchetan2u Please correct the highlighted part to $$x=a_n= 4+2a_{n-1}$$

 Author: bumpbot [ 22 Nov 2022, 08:50 ] Post subject: Re: In a certain sequence, the term an is defined as the value of x that 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).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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