What is the sum of a 7-term geometric series if the first term is −11, the last term is −171,875, and the common ratio is −5?

−143231

The general term of a geometric series can be described by the formula:

an=arn−1

where the initial term is a and common ratio r.

Then we find:

So dividing both ends by (1−r) we find:

N∑n=1an=a(1−rN)1−r

In our example, N=7, a=−11 and r=−5

So:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204