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Lisa [10]
2 years ago
12

Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive fo

rmula for a general term in the sequence. Explain in detail how you found both formulas.
Mathematics
2 answers:
Virty [35]2 years ago
7 0

Answer:

Let the first five terms of a sequence be, 4,8,12,20,24

Ok, let me explain the meaning of term explicit and Recursive formula.

Explicit formula ,is the general formula to find any  term of the sequence.

And, Recursive formula, is the method by which, we can find the nth term of the sequence if (n-1)th term of the sequence is known.

So,the explicit formula for the sequence is,

y = 4 n, where , n is any natural number.

And the recursive formula is .

y = 4 (n-1), with the help of (n-1)th term we can find nth term.

First term =4=4 × 1

Second term =8 =4 × 2

Third term =12=4×3

Fourth term =16 =4 × 4

.....................

...........................

.................................

(n-1) th term =4 × (n-1)

nth term =4 × n

Applying the simple procedure by looking at the first , second and the way the next term goes , the general and recursive formula is obtained.

As, you said you don't want simpler sequence

Consider the first five terms of the sequence, 0, 3,8,15, 24.

Explicit formula =n² + 2 n

Recursive formula=(n-1)²+2(n-1)

If,you will look at the sequence, it is neither Arithmetic nor geometric .

First term =0=0²+0×0

Second term =3=1+2=1²+2 × 1

Third term =8=4+4=2²+2×2

Fourth term =15=9+6=3²+2×3

Fifth term =24=16 +8=4²+2×4

So, Explicit formula= n²+ 2 n, where n is a whole number.

Valentin [98]2 years ago
6 0

Answer: The answer is 5, 10, 20, 40 and 80.

Step-by-step explanation:  We are to write the first five terms of a sequence, along with the explicit and recursive formula for the general term of the sequence.

Let the first five terms of a sequence be  5, 10, 20, 40 and 80. These terms are taken from a geometric sequence with first term a_1 5 and common ratio r=2.

Therefore, we have

a_2=a_1\times r,\\\\a_3=a_2\times r,\ldots

Therefore, the recursive formula is

a_{n+1}=2a_n,~~a_1=5.

And explicit formula is

a_n=a_1r^{n-1}.

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Inessa [10]
A △  Has to have 180º so 72+56 b would have to be appx. 52degrres 
8 0
2 years ago
The area of a square can be tripled by increasing the length and width by 10 inches. What is the original length of the square?
trapecia [35]
The new square has length: 10 + l, where l is the original length of the square, and it's area is (10 + l)^2;
So, we solve the equation: 3 x l^2 = (10 + l)^2;
Then, 3 x l^2 = 100 + 20 x l + l^2;
Finally, 2xl^2 - 20xl - 100 = 0;  / ÷2;
l^2 - 10l - 50 = 0 (we use the quadratic equation formula);
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5 0
2 years ago
Lines a and b are parallel. What is the measuee of angle S?
WITCHER [35]

Answer:

The measure of angle s is 22°

Step-by-step explanation:

Given:

  • Horizontal lines A and B are parallel and are intersecting because a line is going through the both of them.
  • Top right angle of line A is labeled to be 158°, while the top left angle in line B is labeled S° indicating this variable is the missing degrees.

To find:

  • The angle of S, in degrees.

∠1 and 158° are both on a straight line and supplementary.

(Supplementary angles are those angles that sum up to 180 degrees. )

So solving,

⇒ ∠1=180°-158°=22°         ....> Angles ∠1 and S are interior angles

Due to lines A and B being parallel, all interior lines are equal.

As a result, the answer is therefore 22°.

8 0
1 year ago
What's the lcm for 18, 27, 12? I got 648. Am not sure if it is correct. Can you please explain if it is correct or not?
erik [133]

Answer:

Step-by-step explanation:

Put these numbers into their prime factors.

18: 2 * 3 * 3

27: 3 * 3 * 3

12: 2 * 2 * 3

The LCM must have

two 2s

Three 3s

That's it

2*2 * 3 * 3 * 3

LCM = 108

648 might be a multiple of the three, but it's not the smallest one.

108 = 27 * 4

108 = 18 * 6

108 = 12 * 9

6 0
2 years ago
Jose explained to his friend, Emily, that when you multiply matrix A by matrix B, you get the same result as if you multiplied m
Aleks04 [339]

Answer:

yes he is

Step-by-step explanation:

he is correct because say if I multiplied 25 by 10 I would get 250 same would go for if I multiplied 10 by 25 I still would get 250.

I hope this helps

5 0
2 years ago
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