If $x$ is the first number in the progression, and $r$ is the common ratio between consecutive terms, then the first four terms in the progression are

$\{x,xr,xr^2,xr^3\}$

We want to have

$\begin{cases}xr^2-x=12\\xr^3-xr=36\end{cases}$

In the second equation, we have

$xr^3-xr=xr(r^2-1)=36$

and in the first, we have

$xr^2-x=x(r^2-1)=12$

Substituting this into the second equation, we find

$xr(r^2-1)=12r=36\implies r=3$

So now we have

$\begin{cases}9x-x=12\\27x-3x=36\end{cases}\implies x=\dfrac32$

Then the four numbers are

$\left\{\dfrac32,\dfrac92,\dfrac{27}2,\dfrac{81}2\right\}$

4 0

3 years ago

The balance after the grace period is $25,000. A payment of $5,000 is made on the 10th day. A payment of $5,000 is made on the 2

MariettaO [177]

The average daily balance after 20 days is; $1750

<h3>Average Balance</h3>

The initial balance after grace period is; $25,000

Afterwards, A payment of $5,000 each is made on the 10th and 20th day.

Hence, the total balance after 20 days is;

= $25,000 + $5000 + $5000

= $35,000.

The average daily balance is therefore the quotient of $35,000 and 20 days

The average daily balance = $35,000/20

Average daily balance = $1750