A sequence an defined such that an = a(n - 1) - a(n - 2), where n is

Question

A sequence  a_n  defined such that  a_{n} = a_{n-1} - a_{n-2} , where n is a positive integer greater than 2. What is the value of  a_5 ?

(1)  a_{4} - a_{3} = 3 
(2)  a_{14} = -3

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A sequence  A_n  is there such that  A_{n}=A_{n-1}-A_{n-2}  where  n  are integers greater than  2 . What is the value of  A_5 ?

(1)  A_{4} - A_{3}=3 
(2)  A_{14}=1

Oppenheimer1945 · Answer

ao=x, a1=y, a2=y-x, a3=-x, a4=-y, a5=x-y, a6=x...

WHat is  a5=x-y ?

S1)  a4-a3=a5=3   (Suff)

S2)  a14=1=a8=a2=y-x ; Hence  a5=-1  (suff)

D)

Rohan271 · Answer

How is option 2 sufficient?

Posted from my mobile device

Oppenheimer1945 · Answer

Because the sequence is periodic.

a1=a6, an=a_{n+6}

Ddefines · Answer

Didn't understand the 2nd one yet, Bunuel can you please make it a bit easy to understand?

Bunuel · Answer

A sequence  a_n  defined such that  a_{n} = a_{n-1} - a_{n-2} , where n is a positive integer greater than 2. What is the value of  a_5 ?

a_{3} = a_{2} - a_{1} ;
 a_{4} = a_{3} - a_{2} = (a_{2} - a_{1}) - a_{2} = -a_{1} ;
 a_{5} = a_{4} - a_{3} = (-a_{1}) - (a_{2} - a_{1}) = -a_{2} ;
 a_{6} = a_{5} - a_{4} = (-a_{2}) - (-a_{1})=-(a_{2} - a_{1}) = -a_{3} ;
 a_{7} = a_{6} - a_{5} = -(a_{2} - a_{1}) - (-a_{2})=a_{1} = -a_{4} ;
 a_{8} = a_{7} - a_{6} = a_{1} - (a_{1} - a_{2})=a_{2} = -a_{5} ;
and so on.

(1)  a_{4} - a_{3} = 3

Above we we got that  a_{5} = a_{4} - a_{3} , hence  a_{5} = 3 . Sufficient.

(2)  a_{14} = -3

a_{14} = -a_{11}=a_8=-a_5=-3 . Hence  a_{5} = 3 . Sufficient.

Answer: D.

A sequence an defined such that an = a(n - 1) - a(n - 2), where n is

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GMAT Data Sufficiency (DS) Questions

A sequence an defined such that an = a(n - 1) - a(n - 2), where n is

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards