Mathematics, 10.03.2022 05:40 Aaraar

For each sequence, write an explicit and a recursive formula. NO LINKS a. 16, 4, 1, 1/4, 1/16, . . .

b. -2, 5, 12, 19, 26, . . .

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Answer from: husamramadan83

a. explicit: an = 16(1/4)^(n-1); recursive: a[1] = 16, a[n] = 1/4·a[n-1]

b. explicit: an = -2 +7(n -1); recursive: a[1] = -2, a[n] = 7+a[n-1]

Step-by-step explanation:

Finding sequence formulas is all about finding and matching patterns. It is generally pretty easy to subtract one term from the next to see if there is a common difference. If the differences are not constant, but terms have the same ratio. then the sequence is geometric.

The forms for explicit and recursive formulas for arithmetic and geometric sequences are shown here. All you need to do is fill in the values of the first term (a1) and common difference (d) or common ratio (r).

Arithmetic sequence formulas:

explicit formula:

a_n=a_1+d(n-1)

recursive formula:

$a_1 = \text{[first term]};\ a_n=d+a_{n-1}$

Geometric sequence formulas:

explicit formula:

$a_n=a_1\cdot r^{n-1}$

recursive formula:

$a_1 = \text{[first term]};\ a_n=r\cdot a_{n-1}$

The first term is 16. There is no common difference, but the common ratio is 4/16 = 1/4.

explicit formula: an = 16(1/4)^(n-1)

recursive formula: a[1] = 16; a[n] = 1/4·a[n-1]

The first term is -2. The common difference is 5-(-2) = 7.

explicit formula: an = -2 +7(n -1)

recursive formula: a[1] = -2; a[n] = 7 +a[n-1]

_____

Additional comment

Term numbers are generally identified by subscripts on the variable. When writing in plain text, subscripts are difficult to create, so we simply write the subscript next to the variable name: an, a1. This is less satisfactory when there is arithmetic in the subscript, as in the recursive formulas. For those, we have written the plain text formulas using square brackets to show the term numbers: a[1], a[n], a[n-1].

The recursive formula for a given term is defined in terms of the previous term in the sequence. In order for that to work, there needs to be a definition of the first term. We have referred to that generically as a1, but the meaning of a1 = a1 in the recursive formula is maybe no so clear. That is why we used a1 = [first term]. The intention is that [first term] be understood to mean the numerical value of the first term of the sequence.

In short, these problems are worked by finding the common ratio or difference, identifying the first term of the sequence, and filling those two values into the generic formulas.

Answer from: Quest

incomplete question. how do you expect anyone to you when you do not post the question in its entirety?

Answer from: Quest

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle

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For each sequence, write an explicit and a recursive formula. NO LINKS a. 16, 4, 1, 1/4, 1/16, . ....