How many calories are in 1 cup of chocolate ice cream
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a) You have to find the greatest common factor for the values 45 and 54
To do so you have to determine the factors for each value and determine the highest value both numbers are divisible for.
Factors of 45 are
1, 3, 5, 9, 15, 45
Factors of 54 are
1, 2, 3, 6, 9, 18, 27, 54
The greatest common factor is 9, this means that you can divide both numbers by 9 and the result will be an integer:
b) Given the addition
You have to factorize the adition using the common factor.
That is to "take out" the 9 of the addition, i.e. divide 45 and 54 by 9 and you get the result (5+6) but for this result to be equvalent to the original calculation, you have to multiply it by 9
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:
- Money received in first four months: $50, $52, $55, %59.
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:
- The first term of a recursive formula is a₁ and the formula for the nth term uses the first term and the common difference, d. One example of a recursive formula is
.
- A formula for the nth term in an explicit formula would include the initial term a₁, the common difference d, and the term number, n. The equation
.
To learn more about arithmetic Progressions, refer to the link: brainly.com/question/6561461
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