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suter [353]
1 year ago
15

Write the first five terms of the recursively defined sequence. a1 = 6, ak 1 = 1 3 ak2

Mathematics
1 answer:
vova2212 [387]1 year ago
7 0

The first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608

For given question,

We have been given the recursive formula of a sequence.

a_{k+1}=\frac{1}{3}{a_k}^2

Also, the first term of the sequence is,

a1 = 6

Substitute k = 1 in given recursive formula.

⇒ a_{1+1}=\frac{1}{3}{a_1}^2

⇒ a2 = 1/3 (6)²

⇒ a2 = (1/3) × 36

⇒ a2 = 12

Substitute k = 2 in given recursive formula.

⇒ a_{2+1}=\frac{1}{3}{a_2}^2

⇒ a3 = (1/3) × (12)²

⇒ a3 = (1/3) × 144

⇒ a3 = 48

Substitute k = 3 in given recursive formula.

⇒ a_{3+1}=\frac{1}{3}{a_3}^2

⇒ a4 = (1/3) × (48)²

⇒ a4 = (1/3) × 2304

⇒ a4 = 768

Substitute k = 4 in given recursive formula.

⇒ a_{4+1}=\frac{1}{3}{a_4}^2

⇒ a5 = (1/3) × (768)²

⇒ a5 = (1/3) × 589824

⇒ a5 = 196608

Therefore, the first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608

Learn more about the recursive formula of sequence here:

brainly.com/question/14457800

#SPJ4

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1. If 5x + 6 = 10, what is the value of 10x + 3?
Digiron [165]
Here the question is simple.
All because, we only need to find the value of x.
We are given two equations.
5x + 6 = 10 and 10x + 3 =?
So, we will find the the value of x in the first equation, so that we can substitute the value of x in the second one and there we are with the answer.
5x + 6 = 10
For finding the value of x, all we have to do is,
Transpose the number 6 to 10
Therefore. 5x = 10 - 6 ( Take the equal sign as The Magic Bridge on which if anyone crosses it , will change its sign.)
So we have,
5x = 4
So x = 4/5 ( Multiplication will change to division after crossing the equal sign)
( Doubtful? Substitute the value of x and try!)
Now that we got the value of x,
We can just simply substitute the value of x in the second equation.
10x + 3 = ?
x = 4/5
10*4/5 +3 => 5 and 10 get canceled to 2 at the numerator.
By normal multiplication and then addition, we will get,
8 + 3 = 11
Hope this helps!!!! :)
6 0
3 years ago
Read 2 more answers
I really need help. Someone please help me with this.
9966 [12]

Answer:

  angles 1, 3, 6, 8 = 142°

  angles 2, 4, 5, 7 = 38°

Step-by-step explanation:

Vertical angles and corresponding angles are congruent, as are alternate interior angles. Hence the angles 1, 3, 6, 8 are all congruent:

  ∠1 = ∠3 = ∠6 = ∠8 = 142°

Each of the remaining angles forms a linear pair with one or another of those, so is its supplement:

  ∠2 = ∠4 = ∠5 = ∠7 = 180° -142° = 38°

7 0
3 years ago
What is 10th term in 3,8,13,18?
skad [1K]
3+5=8+5=13 so if you keep doing this you  will get 48 which is the answer
5 0
3 years ago
When are conclusions said to be​ statistically significant?
mars1129 [50]

Answer:

If the p-value is less than a given significance level, you reject the null hypothesis and accept the alternative hypothesis.

Step-by-step explanation:

Suppose you have a business in which you'd like to make a change to increase your business. After making the change, you can use a significance test it. To conduct a significance test, you make a null hypothesis which states essentially that no effect happened. You also make an alternative hypothesis that states the change had an effect. You then test the two to see which one stands. In a significance test, using the p-value from your sample you compare it to the null and alternative hypotheses. You make a conclusion when:

  • If the p-value is less than a given significance level, you reject the null hypothesis and accept the alternative hypothesis since the evidence is in favor of it.

If the p-value is greater than the significance level, then you fail to reject the null hypothesis and cannot conclude. There isn't evidence in favor of the alternative hypothesis.

8 0
3 years ago
Help help help plssssss
Novay_Z [31]

Answer:

SA = 108π cm²

Step-by-step explanation:

The surface area (SA) of a sphere is calculated as

SA = 4πr² ( r is the radius )

Thus the SA of a hemisphere is

SA = \frac{1}{2} × 4πr² = 2πr²

The area of the circular base = πr²

Then total SA is

SA = 2πr² + πr² = 3πr² = 3π × 6² = 3π × 36 = 108π cm²

5 0
3 years ago
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