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??
This is the concept of a geometric progression (GP). In a GP, every term is related to the previous term by a fixed ratio r.
So \(t_2 = t_1*r\)
\(t_3 = t_2*r = t_1*r*r\) (substituting from above)
\(t_4 = t_3*r = t_1*r*r*r\)
I hope you understand this.
Here, you are given that \(t_{n+1} = t_n *(\frac{1}{2})\)
So r = 1/2
\(t_2 = t_1 * (1/2)\)
\(t_3 = t_1*(1/2)*(1/2)\)
\(t_4 = t_1 *(1/2)^3\)
\(t_5 = t_1 * (1/2)^4\)
Statement 1 gives you \(t_1\) so you get \(t_5\) easily.
Statement 2 gives you \(t_1 - t_5\). You can substitute \(t_5\) from above and get \(t_1\) and then \(t_5\).
Check out this post on GPs:
http://www.veritasprep.com/blog/2012/04 ... gressions/ _________________
Karishma
Veritas Prep GMAT Instructor
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