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e-lub [12.9K]
3 years ago
14

two terms of an arithmetic sequence are a6= 40 and a20= -16. write and explicit rule for the nth term

Mathematics
1 answer:
Gennadij [26K]3 years ago
5 0

Answer:

Tn = 64-4n

Step-by-step explanation:

The nth term of an AP is expressed as:

Tn = a+(n-1)d

a is the common difference

n is the number of terms

d is the common difference

Given the 6th term a6 = 40

T6 = a+(6-1)d

T6 = a+5d

40 = a+5d ... (1)

Given the 20th term a20 = -16

T20 = a+(20-1)d

T20 = a+19d

-16 = a+19d... (2)

Solving both equation simultaneously

40 = a+5d

-16 = a+19d

Subtracting both equation

40-(-16) = 5d-19d

56 = -14d

d = 56/-14

d = -4

Substituting d = -4 into equation

a+5d = 40

a+5(-4) = 40

a-20 = 40

a = 20+40

a = 60

Given a = 60, d = -4, to get the nth term of the sequence:

Tn = a+(n-1)d

Tn = 60+(n-1)(-4)

Tn = 60+(-4n+4)

Tn = 60-4n+4

Tn = 64-4n

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Can someone help me fully simplify this step by step pleaseeeee
JulijaS [17]

2x - 7x + 2 + 1 - 2

2x - 7x + 3 - 2

- 5x + 1

7 0
2 years ago
Suppose f is a function with exponential growth and f(0)=1. Explain why f can be represented by a formula of the form
galben [10]

We are supposed to explain why the given function can be expressed in form f(x)=b^{x}, when f(0)=1.

Since the given function is an exponential function we can express it as  f(x)=a(b)^{x}.

Now let us substitute x=0 in the given function,  

f(x)=b^{x}

f(0)=b^{0}  

f(0)=1  

Let us substitute x=0 in our function.    

f(0) = a(b)^{0}    

f(0) = a\cdot 1                    

f(0)=a  

Upon substituting a=1 in our function we will get,

f(x) = 1(b)^{x}

f(x) =(b)^{x}

Therefore, our function f can be represented by the formula of the form f(x)=b^{x}.

7 0
3 years ago
Read 2 more answers
3/5 t =6<br><br> Pls help I’ll brainlest
Otrada [13]
Simplify both sides then isolate the variable
t=10
4 0
2 years ago
If r || s and M&lt;5 = 128, what’s is M&lt;1??<br><br> A. 128<br> B. 59<br> C. 62<br> D. 64
Fudgin [204]
We have been given that r is parallel to s. Now, if we look at angle 5 and angle 1, we can see that they are corresponding angles on parallel lines. Corresponding angles are ALWAYS equal, so therefore, your answer is 128 degrees; option A! :)

Hope this helped!
7 0
3 years ago
How do I solve this??
WITCHER [35]

Answer:

Step-by-step explanation:

Formula

Sn = (a + a + (n - 1)*d) * n / 2

Givens

Sn = 60

a =  3

Solution

You want integer values for d and n

60 = (2*a + (n - 1)*d) * n/2           Multiply both sides by 2

120 = (2*3 + (n - 1)*d ) * n    

120 = (6 + n*d - d) * n

120 = 6n + n^2*d - d*n

This gives some really wild results. I will list all of them here. and then discuss them.

These are the ones that give results without any question and are correct.

n         d         tn

2         54         3  57

3          17         3    20   37

4           8         3    11   19   27

Here are some that are the gift of the equation

20         0           3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Now the equation says the following 3 are correct, but are they? Can you have a negative n? The equation says yes, but I doubt your instructor will.

-5         5          

-1         63

-2        22

You can bring these up if you are in a classroom. I wouldn't if you have to submit this to a computer which has absolutely no ability whatever to think about exceptions. Even the 20 0 is one I wouldn't use.

7 0
3 years ago
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