Answer:
Step-by-step explanation:
we know that
In an <u><em>Arithmetic Sequence</em></u> the difference between one term and the next is a constant and this constant is called the common difference
we have
Let
The common difference is
We can write an Arithmetic Sequence as a rule
where
a_n is the nth term
d is the common difference
a_1 is the first term
n is the number of terms
Find the 63rd term of the arithmetic sequence
we have
substitute
Money received in tenth month: $104
Difference between explicit formula and a recursive formula is: the use of (n-1)th term, nth term and the common difference (d) brings a great difference between the two formulae of an arithmetic progression.
<h3>What is arithmetic progression?</h3>A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
To find: Money received in tenth month.
Finding:
As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.
That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.
Thus, for the tenth month, we can use the formula of recursion, given by: , n ≥ 1.
For a₁ = 50, a₂ = a₁ + 2
=> a₂ = 50 + 2
This way, a₅ = a₄ + 5
=> a₅ = 59 + 5 = 64
a₆ = a₅ + 6
=> a₆ = 64 + 6 = 70
a₇ = a₆ + 7
=> a₇ = 70 + 7 = 77
a₈ = a₇ + 8
=> a₈ = 77 + 8 = 85
a₉ = a₈ + 9
=> a₉ = 85 + 9 = 94
a₁₀ = a₉ + 10
=> a₁₀ = 94 + 10 = 104
Thus, the payment received in tenth month will be $104.
(b) Difference between explicit formula and recursive formula of an arithmetic progression:
To learn more about arithmetic Progressions, refer to the link: brainly.com/question/6561461
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Answer: See the figure attached.
Step-by-step explanation:
Observe the figure attached. The vertices of the triangle ABC have the following coordinates:
A(2,5); B(6,2) and C(3,-5)
To graph the image (in this case we can identify it as A'B'C'), you must use the rule →
.
Then, you have to subtract 6 units from the x-coordinate of each vertex and subtract 4 units from the y-coordinate of each vertex.
Therefore, you get:
Vertex A'→
Vertex B'→
Vertex C'→
Having the vertices of the image A'B'C', you can graph it (See the figure attached).
