alright! so I do have an idea of how to work this out but not when i have a sequence going up to like 200!
so here is my problem:
1/3 + -2/3 + 4/3 + -8/3 +.... +-256/3
Eekk.. yeah so techicnally im suppose to find the R (difference of these equations) and then add the sum of all of it up to -256/3. I know I could spend hours doing that but I do know there has to be a quicker way to do it. >o<
so if anyone could help explain how to do this, it would be greatly appreicated!
and thanks so much for your time :)
so here is my problem:
1/3 + -2/3 + 4/3 + -8/3 +.... +-256/3
Eekk.. yeah so techicnally im suppose to find the R (difference of these equations) and then add the sum of all of it up to -256/3. I know I could spend hours doing that but I do know there has to be a quicker way to do it. >o<
so if anyone could help explain how to do this, it would be greatly appreicated!
and thanks so much for your time :)
-
The equation for this is: a(r^n-1)/(r-1) where a is the first term, r is the common ratio, and n is the number of terms.
The first term a is obviously 1/3. The ratio r is (-2/3)/(1/3) = -2. The terms are in the form (1/3)(-2)^x for the numbers 0 through 8, so there are 9 numbers.
Plug in the values: a = 1/3, r = -2, and n = 9.
The sum is (1/3)((-2)^9 -1)/(-2-1) = (1/3)(-512-1))/(-3) = (-513)/(-9) = 57.
As a side note, I think the last term needs to be a positive 256/3.
Please choose best answer.
The first term a is obviously 1/3. The ratio r is (-2/3)/(1/3) = -2. The terms are in the form (1/3)(-2)^x for the numbers 0 through 8, so there are 9 numbers.
Plug in the values: a = 1/3, r = -2, and n = 9.
The sum is (1/3)((-2)^9 -1)/(-2-1) = (1/3)(-512-1))/(-3) = (-513)/(-9) = 57.
As a side note, I think the last term needs to be a positive 256/3.
Please choose best answer.