In the sequence 1, 2, 4, .... an, every nth term for n 1 is created

Question

In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created by the equation  a_n=a_{(n−1)}∗2 . By what percent is the 11th term greater than the 9th term in this sequence?

A. 100%
B. 200%
C. 300%
D. 400%
E. 800%

sowragu · Answer

Since its a GP, the property will hold true for the entire sequence. For instance the percent difference between 1st term and 3rd term is equal to the question stem.

Hence 4/1 = 4 which is 400%

IMO D.

stonecold · Answer

Its a Gp series so 11 term = a^10 ; 9th term = a^8
so difference = 3*2^8 => percent gap = 2^8*3/2^8 *100 = 300 %
hence c is correct

manishtank1988 · Answer

1, 2, 4, 8, 16, 32, 64, 128, 256(9th term), 512, 1024(11th term)
Therefore,  *100 =  *100 = 300%

generis · Answer

a_1 = 1, a_2 = 2, a_3 = 4

Using  a_n=a_{(n−1)}∗2

a_1 = 1 
 a_2 = 2 
 a_3 = 4 = (2 * 2) 
 a_4 = 8 = (2 * 2 * 2) 
 a_5 =16 = (2 * 2 * 2 * 2) 
 a_6=32=(2 * 2 * 2 * 2*2)

By definition, a geometric sequence has a common ratio.

The geometric expansion from  a_2  to  a_4  has the same ratio as the geometric expansion from  a_{212}  to  a_{214} , or the expansion between any two terms, 9 ^{th}  and 11 ^{th}  included.

In other words,  a_{n+2}  will be the same percent greater than  a_{n}  no matter which terms you choose.

So:  a_4  is what percent greater than  a_2 ?

Percent increase =  \frac{New-Old}{Old} * 100

\frac{8 - 2}{2} =\frac{6}{2} * 100  = 300 percent

Answer C

NNURP · Answer

KEY WORD: Greater than...

JannikHeine · Answer

I would just say that every GM sequence within a GM sequence holds the same percentage difference - so difference between first and third term is same as the difference between 9th and 11th term 
--> therefore 300%

bumpbot · Answer

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In the sequence 1, 2, 4, .... an, every nth term for n > 1 is created

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