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# In the sequence 1, 2, 4, 8, 16, 32, …, each term after the

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General Discussion
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Thanks Bunuel for the detailed explanation.
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GWD set 4-Q15 concept question. [#permalink]
In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5?
(1) t3 = 1/4
(2) t1 - t5 = 15/16

I sloved this question, but I heard antoher theory that can solve this question.
The theory is that tn+1 = tn / 2 equals tn=t1*(1/2)^n-1
And I don't understand how this works.
Can some explain how this concept work??
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Re: GWD set 4-Q15 concept question. [#permalink]
2
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sehosayho wrote:
In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5?
(1) t3 = 1/4
(2) t1 - t5 = 15/16

I sloved this question, but I heard antoher theory that can solve this question.
The theory is that tn+1 = tn / 2 equals tn=t1*(1/2)^n-1
And I don't understand how this works.
Can some explain how this concept work??

Hi, it is very simple.

The theory is that tn+1 = tn / 2 equals tn=t1*(1/2)^n-1. In this theory they just generalize it.

Given -- tn+1 = tn/2

Putting n = n- 1

tn= t(n-1) *1/ 2 ----- consider this first equation.
while

t(n-1) = t(n-2)*1/2 ----- consider this 2nd equation.

if you put t(n-1) in first equation

tn = t(n-2) * 1/ 2^2

so when we need t1 on the right hand side.

tn=t1*(1/2)^n-1

Easy way to understand is ---

t2 = t1/2

t3 = t2 / 2

t3 = t1* 1/2^2

So on generalization

tn = t1* 1/ 2^(n-1)

Hope I make it clear.
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Re: GWD set 4-Q15 concept question. [#permalink]
bhatiamanu05 wrote:
sehosayho wrote:
In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5?
(1) t3 = 1/4
(2) t1 - t5 = 15/16

I sloved this question, but I heard antoher theory that can solve this question.
The theory is that tn+1 = tn / 2 equals tn=t1*(1/2)^n-1
And I don't understand how this works.
Can some explain how this concept work??

Hi, it is very simple.

The theory is that tn+1 = tn / 2 equals tn=t1*(1/2)^n-1. In this theory they just generalize it.

Given -- tn+1 = tn/2

Putting n = n- 1

tn= t(n-1) *1/ 2 ----- consider this first equation.
while

t(n-1) = t(n-2)*1/2 ----- consider this 2nd equation.

if you put t(n-1) in first equation

tn = t(n-2) * 1/ 2^2

so when we need t1 on the right hand side.

tn=t1*(1/2)^n-1

Easy way to understand is ---

t2 = t1/2

t3 = t2 / 2

t3 = t1* 1/2^2

So on generalization

tn = t1* 1/ 2^(n-1)

Hope I make it clear.

Thanks! I considered your explanation and got the idea.
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Re: GWD set 4-Q15 concept question. [#permalink]
sehosayho wrote:
In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5?
(1) t3 = 1/4
(2) t1 - t5 = 15/16

I sloved this question, but I heard antoher theory that can solve this question.
The theory is that tn+1 = tn / 2 equals tn=t1*(1/2)^n-1
And I don't understand how this works.
Can some explain how this concept work??

Merging similar topics. Please refer to the solutions above.

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Re: In the sequence 1, 2, 4, 8, 16, 32, , each term after the [#permalink]
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Re: In the sequence 1, 2, 4, 8, 16, 32, , each term after the [#permalink]
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