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3 years ago

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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consider this sum of 36 + 45 Use the distributive property to rewrite the sum as a product of a whole number other than one and

DaniilM [7]

Answer:

9(4+5)

Step-by-step explanation:

Find the common divider of 36 and 45 and put the numbers in the brackets

8 0

3 years ago

A party cap is in the form of a frustum. The radii of its ends are 10cm and 30 cm. The volume of the cap is 9100. What is the he

Vsevolod [243]

Answer:

4.46cm

Step-by-step explanation:

Volume of a frustum is expressed as;

V = (1/3) * π * h * (r₁² + r₂² + (r₁* r₂))

h is the height of the frustum

r₁ and r₂ are the radii of its ends

V is the volume

Given

V = 9100cm₃

r₁ = 10cm

r₂ = 30cm

Substitute

9100 = (1/3) * (3.14) * h * (10² + 30² + (10* 30))

9100 = 1/2(3.14)*h*(100+900+300)

9100 = 1.57*h*(1300)

9100 = 2,041h

h = 9100/2,041

h = 4.46cm

Hence the height of the cap is 4.46cm

3 0

3 years ago

River C is 100 miles longer than River D. If the sum of their lengths is 5,500 miles, what is the length of each river?

Yuki888 [10]

Answer:

river C is 2850 and river B is 2650

8 0

3 years ago

Can you please help

ch4aika [34]

Answer:

6 teaspoons

Step-by-step explanation:

he used the double of cups of flour. so the number of tespoons also doubles

3 0

3 years ago

What is the result of isolating x2 in the equation below?(x + 1)2 + ( -8)2 =9A. x2 = -y2 - 2x +16y - 56B. x2 = y2 +2x+16y +56C.

Anit [1.1K]

The expression we have is:

$(x+1)^2+(y-8)^2=9$

Step 1. Use the binomial square formula:

$(a+b)=a^2+2ab+b^2$

Applying this formula to the first binomial squared:

$x^2+2x+1+(y-8)^2=9$

Step 2. Apply the formula for the square of a binomial to the second binomial:

$x^2+2x+1+y^2+2(y)(-8)+(-8)^2^{}=9$

In this case, we have some operations to solve before we move on to isolating x. So we solve the operations:

$x^2+2x+1+y^2-16y+64^{}=9$

Step 3. Move the terms that are not x squared to the right side of the expression. Remember that when we move one term from one side of the equation to the other, the term must change its sign. We get the following:

$x^2=9-2x-1-y^2+16y-64$

Step 4. Combine like terms and arrange terms in order from the greatest exponent to the lowest and leave the independent term at the end:

$x^2=-y^2-2x+16y-56$

And that is the final result, which is option A.

Answer: Option A.

3 0

2 years ago