What are the explicit equation and domain for a geometric sequence with a first term of 4 and a second term of −8?

Question

anonymous · Answer

@mathmale finally

mathmale · Answer

As before, you need to identify the first term.  That's relatively easy.  

Next, you need to identify the common ratio.  In other words, you start with the first term, 4, and determine BY WHAT NUMBER you must multiply 4 to obtain -8. 

Think of this as an algebraic equation:  -8 = 4r.  How would you solve for r?  What is r?

anonymous · Answer

divide by -8

mathmale · Answer

If 4r=-8, then wouldn't it be more appropriate to divide both sides of this equation by 4?

Do so, please.  r = ?

anonymous · Answer

r=2

mathmale · Answer

4r     -8
--- = --- = ?
   4        4

mathmale · Answer

4r     -8
--- = --- = ?
   4        4

anonymous · Answer

-2

mathmale · Answer

Once you have a and r, you're in a position to write out the geometric sequence.

The general form, as you'll remember, is $$\sum_{n=1}^{infinity}a*r ^{n-1}$$

mathmale · Answer

So, knowing a and r now, write out the geometric series formula (borrow my expression, above).

anonymous · Answer

thank you ttyl

mathmale · Answer

OK!  Please come back and finish this problem whenever you can.