write a formula for the nth term in the geometric series
-6, -3/2, -3/8, -3/32, -3/128, -3/512

Question

write a formula for the  nth term in the geometric series
-6, -3/2, -3/8, -3/32, -3/128, -3/512

anonymous · Answer

The nth term of a geometric series is written as this: |
dw:1339328890132:dw|
So, the first thing we must find is the common geometric ratio. This is found by: 
|dw:1339328943253:dw|
So what this suggests is that the common geometric ratio is found by a term in the geometric ratio divided by a term that is one less than the term. (example: if 4th term, then divided by 3rd term) So, lets choose some terms from the problem. We could do:
|dw:1339329085581:dw|
As you can see the common geometric ratio is 1/4. So we go back to our initial formula and plug back in the value. Another information needed is the first term, which is -6. So the nth term for the series is this:
|dw:1339329183460:dw|