A biased dice is rolled and the results are recorded in a table
2 answers:
You might be interested in
Answer:
Step-by-step explanation:
Given:
- Series 5+11+17+...+251
To find:
- Summation notation of the given series
Summation Notation:
Where n is the number of terms and is general term.
First, determine what kind of series it is, there are two main series that everyone should know:
- Arithmetic Series
A series that has common difference.
- Geometric Series
A series that has common ratio.
If you notice and keep subtracting the next term with previous term:
- 11-5 = 6
- 17-11 = 6
Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.
Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:
<u>Arithmetic Sequence</u>
Where is the nth term,
is the first term and
is the common difference:
So for our general term:
And for number of terms, substitute = 251 and solve for n:
Now we can convert the series to summation notation as given the formula above, substitute as we get:
wheee
Compute each option
option A: simple interest
simple interest is easy
A=I+P
A=Final amount
I=interest
P=principal (amount initially put in)
and I=PRT
P=principal
R=rate in decimal
T=time in years
so given
P=15000
R=3.2% or 0.032 in deecimal form
T=10
A=I+P
A=PRT+P
A=(15000)(0.032)(10)+15000
A=4800+15000
A=19800
Simple interst pays $19,800 in 10 years
Option B: compound interest
for interest compounded yearly, the formula is
where A=final amount
P=principal
r=rate in decimal form
t=time in years
given
P=15000
r=4.1% or 0.041
t=10
use your calculator
A=22418.0872024
so after 10 years, she will have $22,418.09 in the compounded interest account
in 10 years, the investment in the simple interest account will be worth $19,800 and the investment in the compounded interest account will be worth$22,418.09