In the sequence of positive number x1, x2, x3,. . . what is

[Anne1276]

In the sequence of positive number x1, x2, x3,. . . what is the value of x1??

(1) X (sub j) = X(sub j - 1) / 2 for all integers j > 1

(2) X (sub 5) = X(sub 4) / ((X sub 4) + 1)


This is a sequence problem with X sub 5 representing the 5th member of the series, etc,, etc. Thanks!

I am not great with sequences so I didn't know where to begin.

[Jeff]

Perhaps the most important thing to realize with sequence problems is that once the sequence is definied, if you can find one value in the sequence you can find them all.

My approach to this problem was to use a little algebra to find X(sub 4) then just apply the definition of the sequence we are given to find X (sub 1). In order to keep the notation a little simpler, let me substitute a = x (sub4) and b= x (sub5).

ok , from (1) we get:

b=a/2
a=2b

from (2) we get

b=a/(a+1)

so you have two equations in two unknowns. Substitute and solve:

a/2=a/(a+1)
a=2a/a+1
a^2+a=2a
a^2-a=0
a(a-1)=0

a=0,1.

The root a=0 is what might be called a trival answer (every element of the sequence =0) and no doubt 0 was not an answer choice. Instead consider:

X(sub 4) = a = 1.
So what does X(sub 1) equal? Well, each element in the sequence is half the one before it, so x(sub4)=1, x(sub3)=2,x(sub2)=4,x(sub4)=8.

Jeff

[maaz_gmat]

Perhaps the most important thing to realize with sequence problems is that once the sequence is definied, if you can find one value in the sequence you can find them all.

My approach to this problem was to use a little algebra to find X(sub 4) then just apply the definition of the sequence we are given to find X (sub 1). In order to keep the notation a little simpler, let me substitute a = x (sub4) and b= x (sub5).

ok , from (1) we get:

b=a/2
a=2b

from (2) we get

b=a/(a+1)

so you have two equations in two unknowns. Substitute and solve:

a/2=a/(a+1)
a=2a/a+1
a^2+a=2a
a^2-a=0
a(a-1)=0

a=0,1.

The root a=0 is what might be called a trival answer (every element of the sequence =0) and no doubt 0 was not an answer choice. Instead consider:

X(sub 4) = a = 1.
So what does X(sub 1) equal? Well, each element in the sequence is half the one before it, so x(sub4)=1, x(sub3)=2,x(sub2)=4,x(sub4)=8.

Jeff

Jeff - Could you explain in more detail? I havent understood how you have even begun solving.... - - ok , from (1) we get:

b=a/2
a=2b

from (2) we get

b=a/(a+1)


Could you please throw light on the same.

Thanks.

[RonPurewal]

stacey solved this one here:
post7712.html#p7712