Answer:
(a) The sum of the previous term and 9
(b) 36, 45, 54
Step-by-step explanation:
Given
Sequence: Arithmetic Progression
![0,9,18,27](https://tex.z-dn.net/?f=0%2C9%2C18%2C27)
Solving (a): Describe the relationship in each term
First, we calculate the common difference (d)
In arithmetic progression:
![d = T_n - T_{n-1}](https://tex.z-dn.net/?f=d%20%3D%20T_n%20-%20T_%7Bn-1%7D)
Take n as 2
![d = T_2 - T_{2-1}](https://tex.z-dn.net/?f=d%20%3D%20T_2%20-%20T_%7B2-1%7D)
![d = T_2 - T_{1}](https://tex.z-dn.net/?f=d%20%3D%20T_2%20-%20T_%7B1%7D)
Where
![T_2 = 9\ and\ T_1 = 0](https://tex.z-dn.net/?f=T_2%20%3D%209%5C%20and%5C%20T_1%20%3D%200)
![d =9-0](https://tex.z-dn.net/?f=d%20%3D9-0)
![d =9](https://tex.z-dn.net/?f=d%20%3D9)
<em>The relationship is: The sum of the previous term and 9</em>
Solving (b): The next three terms
As said in (a) each term is derived from a sum of 9 and the previous term
So, we have:
![Next\ Term = 27 + 9 = 36](https://tex.z-dn.net/?f=Next%5C%20Term%20%3D%2027%20%2B%209%20%3D%2036)
![Next = 36 + 9 = 45](https://tex.z-dn.net/?f=Next%20%3D%2036%20%2B%209%20%3D%2045)
![Next = 45 + 9 = 54](https://tex.z-dn.net/?f=Next%20%3D%2045%20%2B%209%20%3D%2054)
Hence, the next three terms are: 36, 45 and 54
Answer:
t = 20.772
Step-by-step explanation:
r = R/100
r = 6/100
r = 0.06 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(5,200.00/1,500.00) / ( 12 × [ln(1 + 0.06/12)] )
t = ln(5,200.00/1,500.00) / ( 12 × [ln(1 + 0.005)] )
t = 20.772 years
That '3' will stretch the graph vertically, and that +8 will shift the whole graph upward by 8 units. Why not try graphing these 2 functions?
23
%
=
23
100
=
0.23
First we have to think that the symbol
%
=
1
100
so that
23
%
=
23
⋅
(
1
100
)
this is read twenty three percent is equal to twenty three multiplied by one divided by one hundred.
the result is the fraction
23
100
Now, to convert to decimal, simply divide 23 by 100
23
÷
10
=
2.3
and
2.3
÷
10
=
0.23
this is the same as
23
÷
100
=
0.23