Answer:
a[n] = a[n-1]×(4/3)
a[1] = 1/2
Step-by-step explanation:
The terms of a geometric sequence have an initial term and a common ratio. The common ratio multiplies the previous term to get the next one. That sentence describes the recursive relation.
The general explicit term of a geometric sequence is ...
a[n] = a[1]×r^(n-1) . . . . . where a[1] is the first term and r is the common ratio
Comparing this to the expression you are given, you see that ...
a[1] = 1/2
r = 4/3
(You also see that parenthses are missing around the exponent expression, n-1.)
A recursive rule is defined by two things:
- the starting value(s) for the recursive relation
- the recursive relation relating the next term to previous terms
The definition of a geometric sequence tells you the recursive relation is:
<em>the next term is the previous one multiplied by the common ratio</em>.
In math terms, this looks like
a[n] = a[n-1]×r
Using the value of r from above, this becomes ...
a[n] = a[n-1]×(4/3)
Of course, the starting values are the same for the explicit rule and the recursive rule:
a[1] = 1/2
Answer: 3x-180
Step-by-step explanation:
Given: Expression for Revenue = ![5x^2 + 2x - 80](https://tex.z-dn.net/?f=5x%5E2%20%2B%202x%20-%2080)
Expression for Cost = ![5x^2- x + 100](https://tex.z-dn.net/?f=5x%5E2-%20x%20%2B%20100)
If profit is the difference between the revenue and the cost then the expression for profit will be:
Profit = Revenue - cost
![=5x^2 + 2x - 80-(5x^2- x + 100)\\\\=5x^2 + 2x - 80-5x^2+x-100\ \ [\text{Multiply ' - ' sign inside the bracket}]\\\\=2x+x-80-100\\\\=3x-180](https://tex.z-dn.net/?f=%3D5x%5E2%20%2B%202x%20-%2080-%285x%5E2-%20x%20%2B%20100%29%5C%5C%5C%5C%3D5x%5E2%20%2B%202x%20-%2080-5x%5E2%2Bx-100%5C%20%5C%20%5B%5Ctext%7BMultiply%20%27%20-%20%27%20sign%20inside%20the%20bracket%7D%5D%5C%5C%5C%5C%3D2x%2Bx-80-100%5C%5C%5C%5C%3D3x-180)
Hence, the expression represents the profit is 3x-180 .
Answer:
just use the app Math-way it had a feature where you can take a picture of it and it will answer and give an explanation for your problem
Answer:
Step-by-step explanation:
1,4 ,13 , __________, 121
First term = 1
Second term = 1 + 3 = 4
Third term = 4 + 3*3 = 4 + 9 = 13
Fourth term = 13 + 3*3*3 = 13 + 27 = 40
2) 5, 12 , 33 ,_____
First term = 5
Second term = 5 + 7 = 12
Third term = 12 + 7*3 = 12 + 21 = 33
Fourth term = 33 + 7*3*3 = 33 + 63 = 99