Let

where we assume |r| < 1. Multiplying on both sides by r gives

and subtracting this from
gives

As n → ∞, the exponential term will converge to 0, and the partial sums
will converge to

Now, we're given


We must have |r| < 1 since both sums converge, so


Solving for r by substitution, we have


Recalling the difference of squares identity, we have

We've already confirmed r ≠ 1, so we can simplify this to

It follows that

and so the sum we want is

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?
Step-by-step explanation:
since we have the relation (inches/dollars)
4.3 inches down per dollar
per 10 dollars 43 inches down
per half a dollar 2.15 inches down
per 63.60 dollars 273.48 inches down
DB is a median (given). It goes from vertex point D to midpoint B.
The point B is the midpoint of segment AC. So B cuts AC into two equal halves: AB and AC
Meaning AB = AC
AC = AB+BC ... segment addition postulate
AC = AB+AB ... substitution; replace BC with AB (valid because AB = AC)
AC = 2*AB
2*AB = AC
2*AB = 50 ... substitution; replace AC with 50
2*AB/2 = 50/2 ... divide both sides by 2
AB = 25 which is the answer
Mot enough information given.
The rule might be
-- add 6
or
-- double and add 8
or
-- square
or
-- multiply by -2 .
We need one more term to determine what the rule is for calculating the next term from the previous one.
The
Answer:
I have no idea
Step-by-step explanation:
5xt789v