The explicit formula is a(n) = 15(n – 10)
<u>Solution:</u>
Given, a term a(19) = 135 and common difference d = 15
We have to find the explicit formula.
Now, we know that, a(n) = a + (n – 1)d where a(n) is nth term, a is first term, d is common difference,
So, for a(19)

Now, we know that, an explicit formula is an expression for finding the nth term,
So, in our problem, expression for finding nth term is a + (n – 1)d

Hence, the explicit formula is a(n) = 15(n – 10).
In order to determine the balance of the account, use the following formula for the amount of money obtained after t years, basen on a compound interest:

where,
P: principal = $12,500
A: amount earnt after t years = ?
r: interest rate in decimal form = 0.045 (4.5%)
n: times at year for the compund interes = 4 (quaterly)
Replace the previous values of the parameters into the formula for A and simplify:

Hence, the balance after 8 years is approximately $17,880.64 in the account.
The interest earnt by the account is given by the difference between the previous result and the principal invesment:
I = $17,880.64 - $12,500 = $5,380.64
Hence, the interest earnt is $5,380.64
A number is rational if it can be written as the ratio of two integers.
The ratio of two integers is a fraction, and you just did it. Your number
is the ratio of 1 to 8 . It's about as rational as you can get.
<span>Here's a fun fact that's easy to remember:
<em>ANY</em> number that you can write down on paper, completely,
with digits
and a decimal point or a fraction bar if you need them, is
rational.</span>