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Explicit arithmetic formula for the sequence 16,13,10,7,4


It is adding negative3 every time not subtracting three because you can't do that when working with arithmitic

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Posted in Mathematics

A certain forest covers an area of 2,000 square kilometers. Suppose that each year this area decreases by 6%. What is the function that best represents the area of the forest each year and how much area remains after 12 years? Round your answer to the nearest square kilometer. Hint: Use the formula, f(x) = P(1 + r)x

For the answer to the question above, I think the formula you is wrong. The x must be in exponential form. It must look like this

f(x) = P(1 + r)^x
Now we can solve.

Given:
P = 2000
r = -0.06

f(x)  =  2000 (1 - 0.06)^x
       =  2000 (0.94)^x


         
2000 (0.94)¹² = 

2000 (0.476)  = 
The answer is 
951.8 square kilometers.
                   

Posted in Mathematics

Which answer describes the type of sequence? −99, −88, −66, −55, ... A. arithmetic B. neither arithmetic nor geometric C. geometric

Here, Geometric ratio, r = -88/-99 or -66/-88 which is 8/9 or 6/8. As they are not equal, it is not a geometric.

Now, Arithmetic difference, d = -88-(-99) or -66-(-88) which is 11 or 22. As they are not equal, it is not a Arithmetic.

So, it's neither an Arithmetic nor a Geometric.

Option B is your answer!

Hope this helps!

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What is the common ratio for the geometric sequence? 54, 36, 24, 16...

Geometric ration, r = 36/54 or 24/36 which is equal to 2/3

So, your final answer is 2/3

Hope this helps!

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Posted in Mathematics

What is the common difference d of the sequence? 9, −8, −25, −42, −59, ... d =

Common difference, d = -8-9 or -25-(-8) which is equal to -17

So, your final answer is -17

Hope this helps!

Posted in Mathematics

What is the next 3 terms in the following sequence, 5.5,6.7,7.9,9.1

10.3, 11.5, 12.7, u keep adding 1.2 every time so u can get the answer, can u make this the brainliest???

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4,-24,144,-864,... whats the 8th term in the sequence?

Are 24 and 864 supposed to be negatives?

If so, that means that each term is multiplied by negative 6.
So, 4 times -6 = -24. Then -24 x -6 = 144. And so on.

So -864 x -6 = 5,184. (5th term)
5,184 x -6 = -31,104. (6th term)
-31,104 x -6 = 186,624. (7th term)
186,624 x -6 = -1,119,744. (8th term)

I think, and hope, that it is correct. Hope this helps! :)

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Posted in Mathematics

What is the explicit rule for this geometric sequence? 4,4/5,4/25,4/125,…

To find the nth sequence you just use this function. (^ being the power of )

f(n) = 4/5^n 

Posted in Mathematics

Write the explicit formula for the sequence 3,5,7,9,11

3+2=5
5+2=7
7+2=9
9+2=11
.
.
.
so d=2
-------------
formula:a(n)=a(1)+(n-1)d
a(n)=3+(n-1)2
a(n)=3+2n-2=2n+1

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Posted in Mathematics

What is an equation that models the sequence 400, 200, 100, 50, ?

N / 2

400 / 2 = 200
200 / 2 = 100
100 / 2 = 50
50 / 2 = 25
25 / 2 = 12.5

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A sequence is defined recursively using the formula f(n + 1) = f(n) – 5 . Which sequence could be generated using this formula? 1, –5, 25, –125, ... 2, 10, 50, 250, ... 3, –2, –7, –12, ... 4, 9, 14, 19, ...

Lets take second number in each sequance as
f(n+1) and first as
 f(n)

for first sequance we get:
25 = -5 -5 which is not true.

second sequance:
50 = 10 -5  again not true.

third sequance
-7 = -2 - 5 which is true. If we use f(n+1) to be -12 and f(n) to be -7 again we will see that formula describes this third sequance.

last one if we check for just in case we will see that it doesn't fallow the formula.

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1. Which best describes the relationship between the successive terms in the sequence shown? 9, –1, –11, –21, … a)The common difference is –10. b)The common difference is 10. c)The common ratio is –9. d)The common ratio is 9. 2. A sequence is defined recursively using the formula f(n + 1) = f(n) – 5 . Which sequence could be generated using this formula? a)1, –5, 25, –125, ... b)2, 10, 50, 250, ... c)3, –2, –7, –12, ... d)4, 9, 14, 19, ...

Q1. The answer is a)The common difference is –10. 

Let's calculate the common difference (c):
c = f(n + 1) - f(n)

9, –1, –11, –21, …
-1 - 9 = -10
-11 - (-1) = -11 + 1 = -10
-21 - (-11) = -21 + 11 = -10


Q2. The answer is 
c)3, –2, –7, –12, ...

f(n + 1) = f(n) – 5
f(n + 1) - f(n) = -5

c = f(n + 1) - f(n)

So, the common difference is: c = -5

Let's check all choices:
a) c = -5 - (-1) = -5 + 1 = -4         INCORRECT
b) c = 10 - 2 = 8                        INCORRECT
c) c = -2 - (-3) = -5
    c = -7 - (-2) = -5
    c = -12 - (-7) = -5                    CORRECT
d) c = 9 - 4 = 5                          INCORRECT

Posted in Mathematics

Find the sum of the first 50 terms of the sequence below. An = 3n + 2

An+1= 3n+3 +2
An+1 - An = 3n+5 -3n-2=3
An is aa arithmetic sequence
its sum is given by:
A0 +A1 +A2 + . . . + An = N(Ao + An) /2
where N = n-0=n
S50= A0 +A1 +A2 + . . . + A50 = 50(Ao + A50) /2

S50 = 50(Ao + A50) /2
Ao=2, A50=150+2=152
S50= 50(Ao + A50) /2

finally
S50=25*154=3850

Posted in Mathematics

640, 160, 40, 10, ... Which correctly describe the graph of the geometric sequence? Check all that apply. The graph will show exponential growth. The graph will appear linear. The domain will be the set of natural numbers. The range will be the set of natural numbers. The graph will show exponential decay.

The function is y = 640/ 4^x and the graph decreases exponentially from 640 (for x =0) and asymptotically approacdhes zero (when x becomes larger and larger). This is an exponential decay.

Answer: the last option of the list. The graph will show exponential decay


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Triangular numbers can be represented with equilateral triangles formed by dots. The first five triangular numbers are 1, 3, 6, 10, and 15. Is there a direct variation between a triangular number and its position in the sequence? Explain your reasoning.

Position in the sequence    triangular number    relation

1                                          1                              1 = 1*(1+1)/2

2                                          3                              3 = 2(2+1)/2

3                                          6                              6 = 3(3+1)/2

4                                         10                            10 = 4(4+1)/2

5                                         15                              15= 5(5+1)/2

Call n the position in the sequence, then the triangular number is: n(n+1)/2
 



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