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andriy [413]
3 years ago
12

Find the next term is in the explicit and recursive rule for the in term of the sequence. NO LINKS!!!

Mathematics
1 answer:
BARSIC [14]3 years ago
7 0

9514 1404 393

Answer:

  5) 729, an=3^n, a[1]=3; a[n]=3·a[n-1]

  6) 1792, an=7(4^(n-1)), a[1]=7; a[n]=4·a[n-1]

Step-by-step explanation:

The next term of a geometric sequence is the last term multiplied by the common ratio. (This is the basis of the recursive formula.)

The Explicit Rule is ...

  a_n=a_1\cdot r^{n-1}

for first term a₁ and common ratio r.

The Recursive Rule is ...

  a[1] = a₁

  a[n] = r·a[n-1]

__

5. First term is a₁ = 3; common ratio is r = 9/3 = 3.

Next term: 243×3 = 729

Explicit rule: an = 3·3^(n-1) = 3^n

Recursive rule: a[1] = 3; a[n] = 3·a[n-1]

__

6. First term is a₁ = 7; common ratio is r = 28/7 = 4.

Next term: 448×4 = 1792

Explicit rule: an = 7·4^(n-1)

Recursive rule: a[1] = 7; a[n] = 4·a[n-1]

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Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its corre
Ad libitum [116K]

Answer:

1/3 is the answer.

Step-by-step explanation:

Tanya prepared 4 different letters to be sent to 4 different addresses.

To solve this we can do the following:

The probability that the 1st letter is in the right envelope is = \frac{1}{4}

The probability that the 2nd letter is in the wrong envelope is = \frac{2}{3}

The probability that the 3rd letter is in the wrong envelope is = \frac{1}{2}

The probability that the 4th letter is in the wrong envelope is = 1

So, the answer becomes: \frac{1}{4}\times \frac{2}{3}\times \frac{1}{2}\times1 = \frac{1}{12}

As we need 4 correct letters in the envelope, we will multiply by 4:

\frac{1}{12}\times4=\frac{1}{3}

3 0
3 years ago
25) Which graph represents the equation below? ) = w+ 2 A ܠܐ 5 4 (2, 4) 3 2 1 (-2,0) -5 -4 -3 -2 -1 0 -1 x 1 2 3 4 5 -2 -3 -4 -5
victus00 [196]

Answer:

Can you attach a pic please ?

Step-by-step explanation:

6 0
3 years ago
Pretest: Unit 5 Question 12 of 21 Use the substitution method to solve the system of equations. Choose the correct ordered pair.
Gala2k [10]

Answer:

(10, - 9 )

Step-by-step explanation:

Given the 2 equations

y = - 2x + 11 → (1)

y = - 3x + 21 → (2)

Substitute y = - 2x + 11 into (2)

- 2x + 11 = - 3x + 21 ( add 3x to both sides )

x + 11 = 21 ( subtract 11 from both sides )

x = 10

Substitute x = 10 into either of the 2 equations and evaluate fir y

Substituting into (1)

y = - 2(10) + 11 = - 20 + 11 = - 9

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3 0
2 years ago
Percent equations the question is blank % of 75 = 30
lubasha [3.4K]

Answer:

40

Step-by-step explanation:

30/75 = .4

4 0
3 years ago
Read 2 more answers
What are the values of the variables in the triangle below? If your answer is not an integer, leave it in simplest radical form.
castortr0y [4]

Answer:

<h2>x = 12</h2><h2 /><h2>y = 4√3</h2>

Step-by-step explanation:

<u>To find x we use cosine</u>

cos∅ = adjacent / hypotenuse

x is the adjacent

8√3 is the hypotenuse

cos 30 = x / 8√3

x = 8√3 cos 30

<h3>x = 12</h3>

<u>To find y we use sine</u>

sin∅ = opposite / hypotenuse

y is the opposite

8√3 is the hypotenuse

sin 30 = y / 8√3

y = 8√3 sin 30

<h3>y = 4√3</h3>

Hope this helps you

5 0
3 years ago
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