Find the first five terms of the sequence.

@mathmale Hello, would you be willing to lend me hand in showing me how to complete this type of equation? I did a similar one but it didn't have the where a1 = 20 on the end.

Question

Find the first five terms of the sequence.

@mathmale  Hello, would you be willing to lend me hand in showing me how to complete this type of equation? I did a similar one but it didn't have the where a1 = 20 on the end.

nicole143 · Answer

$$a_{n} = \frac{ 1 }{ 2 }a _{n} - 1 $$  Where a1 = 20

mathmale · Answer

$$a_{n} = \frac{ 1 }{ 2 }a _{n} - 1\rightarrow a _{n=} \frac{ 1 }{ 2 }a _{n-1}$$ is a bit clearer.   

Here's how you explain this formula:  "The nth term of the sequence in question is equal to one half of the previous term, that is, one half of the (n-1)th term."

mathmale · Answer

So, Nicole, if a-sub-1 is 20, what is a-sub-2?  Hint:  Multiply 20 by (1/2).

mathmale · Answer

$$a _{1}=20 \rightarrow a _{2}=\frac{ 1 }{ 2 }(20)=?$$

nicole143 · Answer

10

Sorry, I left there for a bit.. @mathmale

mathmale · Answer

So:  a-1 is 20;
       a-2 is 10 (half of a-1)
       a-3 is ?

nicole143 · Answer

Yes, thank you!

nicole143 · Answer

Wait, what about to  -1  ? @mathmale

mathmale · Answer

I'm sorry:  my notation is not clear.  I'll draw this sequence instead:|dw:1395622484108:dw|