Answer:
5
Explanation:
Look at the number line and count the number of increments needed to get from point A to B.
Multiply (or distribute) the exponent<span> outside the parenthesis with every </span>exponent<span>inside the parenthesis, remember that if there is no </span>exponent<span> shown, then the </span>exponent<span> is 1. Step 3: Apply the </span>Negative Exponent<span> Rule. </span>Negative exponents<span> in the numerator get moved to the denominator and become positive </span>exponents<span>.</span>
We find the first differences between terms:
7-4=3; 12-7=5; 19-12=7; 28-19=9.
Since these are different, this is not linear.
We now find the second differences:
5-3=2; 7-5=2; 9-7=2. Then:
Since these are the same, this sequence is quadratic.
We use (1/2a)n², where a is the second difference:
(1/2*2)n²=1n².
We now use the term number of each term for n:
4 is the 1st term; 1*1²=1.
7 is the 2nd term; 1*2²=4.
12 is the 3rd term; 1*3²=9.
19 is the 4th term; 1*4²=16.
28 is the 5th term: 1*5²=25.
Now we find the difference between the actual terms of the sequence and the numbers we just found:
4-1=3; 7-4=3; 12-9=3; 19-16=3; 28-25=3.
Since this is constant, the sequence is in the form (1/2a)n²+d;
in our case, 1n²+d, and since d=3, 1n²+3.
The correct answer is n²+3
Answer:
$18,087.23
Step-by-step explanation:
The future worth of the loan in 7 years compounded semiannually is computed as shown below using the future value formula adjusted for semiannual compounding:
FV=PV*(1+r/2)^n*2
FV is the worth of the loan in 7 years which is unknown
PV is the actual amount of loan which is $8,000
r is the rate of interest of 12%
n is the number of years of the loan which is 7 years
the 2 is to show that interest is computed twice a year
FV=8000*(1+12%/2)^7*2
FV=8000*(1+6%)^14
FV=8000*1.06^14=$18,087.23
