The first term in a geometric series is 64 and the common ratio is 0.75. Find the sum of the first 4 terms in the series.

195.25

Step-by-step explanation:

Consider geometric series  S(n) where initial term is a

So S(n)=a+ar^1+...ar^n

Factor out a

S(n)=a(1+r+r^2...+r^n)

Multiply by r

S(n)r=a(r+r^2+r^3...+r^n+r^n+1)

Subtract S(n) from S(n)r

Note that only 1 and rn^1 remain.

S(n)r-S(n)=a(r^n+1  -1)

Factor out S(n)

S(n)(r-1)=a(r^n+1  -1)

The formula now shows S(n)=a(r^n+1  -1)/(r-1)

Now use the formula for the problem

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

more detail

step-by-step explanation: