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3 years ago

Given the third term of an arithmetic sequence less than the fourth term by three. The seventh term

Mathematics

1 answer:

UNO [17]3 years ago

6 0

Answer:

The first term is -6 and common difference is 3

Step-by-step explanation:

The nth term of an arithmetic progression is expressed as;

Tn = a + (n-1)d

T3 = a+2d

T4 = a + 3d

If the third term of an arithmetic sequence less than the fourth term by three

T3 = T4 - 3

a+2d = a+3d - 3

2d - 3d = -3

-d = -3

d = 3

Similarly;

T7 = a+6d

T5 = a+4d

If the seventh term is two times the fifth term, the;

T7 = 2T5

a+6d = 2(a+4d)

a+6d = 2a+8d

Since d = 3

a + 6(3) = 2a + 8(3)

a+18 = 2a + 24

a-2a = 24 - 18

-a = 6

a = -6

Hence the first term is -6 and common difference is 3

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ZanzabumX [31]

1 1/2 * 3/4 =

Change 1 1/2 to an improper fraction = 3/2

3/2 * 3/4 = 6/4 * 3/4

6/4 * 3/4 = 18/4 = 4 2/4 = 4 1/2

The answer is 4 1/2.

Hope this helped☺☺

4 0

3 years ago

Question: A square with sides of length 5 is positioned inside a square with sides of length 7. What is the total area between t

Sergio [31]

Answer:

The total area between the squares is of 24 units squared.

Step-by-step explanation:

Area of a square:

The area of a square of side length l is given by:

$A = l^2$

Area between figures:

The area between two figures is the area of the larger figure subtracted by the area of the smaller figure.

Larger square:

Square with side of length 7. So

$A_l = 7^2 = 49$

Smaller square:

Square with side of length 5. So

$A_s = 5^2 = 25$

What is the total area between the squares? 

$T = A_l - A_s = 49 - 25 = 24$

The total area between the squares is of 24 units squared.

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3 years ago

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irinina [24]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Mary buys a reel of thread for sewing. There are 10 m of thread on the reel. She uses 210 cm. How much is left on the reel in ce

galben [10]

10meters=1000cm
1000-210=890
Mary has 890 centimeters of thread left on the reel.

5 0

3 years ago

Find the term that must be added to the equation x2 6x=1 to make it into a perfect square.

andrezito [222]

The value added to the equation $$x^2-6x=1$ exists $$x^2-6x+9=10$ .

<h3>What is a perfect square?</h3>

A perfect square exists as a number that can be described as the product of an integer by itself or as the second exponent of an integer.

The perfect square trinomial exists

$(a$ ± $b)^2$ = $a ^2$ ± 2ab + $b ^2$

$$x^2-6x=1$

$x^2-2*3x=1$

then $$2ab = 2 * 3*x = 2 * x *3$

The value of a = x and b = 3

$$b^2=3^2=9$

$$x^2-6x+9=1+9$

$$x^2-6x+9=10$

The value added to the equation $$x^2-6x=1$ exists $$x^2-6x+9=10$ .

To learn more about perfect square refer to: brainly.com/question/6946048

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3 0

2 years ago