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PtichkaEL [24]
3 years ago
6

What is the rule for the following sequence: 2, 9, 21, 65

Mathematics
1 answer:
Helga [31]3 years ago
5 0

There is no common ratio or common difference. The first three terms increases more slowly than a cubic, but the last three increase more quickly than the cube of n. The pattern is not obvious to me. When the sequence is cast in recursive terms, you get

... a[n] = (48/13)a[n-2] + (59/39)a[n-1] . . . . a[1] = 2, a[2] = 9

The next term using this rule is 174 34/39, not an integer.

The coefficients p and q for a[n-2] and a[n-1] can be found from

2p+9q=21\\9p+21q=65

_____

Any sequence of 4 numbers can be matched by a polynomial of degree 3 or less. Here, a calculator's polynomial regression function tells us the rule could be

... a[n] = 4.5n³ -24.5n² +49n -27

Using this rule, the next two terms are 168 and 357.

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the greater of two numbers is 1 more than twice smaller. three times greater exceeds 5 times the smaller by 10. find the three n
krek1111 [17]
<h3><u>The value of the greater number is 15.</u></h3><h3><u>The value of the smaller number is 7.</u></h3>

x = 2y + 1

3x = 5y + 10

Because we have a value for x we can plug this value in to find the value of y.

3(2y + 1) = 5y + 10

Distributive property.

6y + 3 = 5y + 10

Subtract 5y from both sides.

y + 3 = 10

Subtract 3 from both sides.

y = 7

We can plug this value back into the original equation to find the value of x.

x = 2(7) + 1

x = 15


7 0
3 years ago
Can you solve this????? Super hard!
Likurg_2 [28]

Answer:

  \textbf{J. }\dfrac{1}{x^2-x}

Step-by-step explanation:

Factor the denominator and cancel the common factor.

  \dfrac{x+1}{x^3-x}=\dfrac{x+1}{x(x^2-1)}=\dfrac{x+1}{x(x-1)(x+1)}=\dfrac{1}{x(x-1)}\\\\=\boxed{\dfrac{1}{x^2-x}}

6 0
3 years ago
6 is 15% of what number? *<br> 70<br> 40<br> 45<br> 50
sveta [45]

Answer:40

Step-by-step explanation:

8 0
3 years ago
I need to know the answer
ladessa [460]

Answer:

b

Step-by-step explanation:

Answer: option (b)

1 billion = 1, 000, 000, 000

In scientific notation, a number is rewritten as a simple decimal multiplied by 10 raised to some power n.

10 =101

100= 102

1, 000 = 103

1, 0000 = 104.

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

Therfore 1 billion can be written as

1 billion =1, 000, 000, 000=10^{9}

Then 1.5 billion =  1.54 10^{9}

Hence option (b) is the correct answer

please give me brilliant answer

thank you

5 0
3 years ago
Connor can travel 2 3/4 miles in 2 1/2 hours. What is his average speed in miles per hour?
Leviafan [203]
Hence the answer is c 1.1 mph

6 0
3 years ago
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