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SashulF [63]
3 years ago
6

The first term of an AP is -7 and the ratio of the eight term to the third term is 7:1 calculate the common difference

Mathematics
1 answer:
alukav5142 [94]3 years ago
4 0

Answer:

the common difference is 6.

Step-by-step explanation:

Given;

first term of an AP, a = -7

let the common difference = d

The third term is written as;

T₃ = a + 2d

The eight term is written as;

T₈ = a + 7d

The ratio of the eight term to third term = 7:1

\frac{T_8}{T_3} = \frac{7}{1} = \frac{a+ 7d}{a + 2d} \\\\7 =  \frac{a+ 7d}{a + 2d}\\\\Recall, a = -7\\\\7 =   \frac{-7+ 7d}{-7 + 2d}\\\\7(-7 + 2d) = -7+ 7d\\\\-49 + 14d = -7 + 7d\\\\14d -7d = -7 + 49\\\\7d = 42\\\\d = \frac{42}{7} \\\\d = 6

Therefore, the common difference is 6.

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8 0
3 years ago
Calculate the midpoint between (2,-5) and (4, -7).
balandron [24]

The midpoint between (2,-5) and (4, -7)  is Option D.(3-6)

Step-by-step explanation:

Given:

Points (2,-5) and (4, -7)

To Find:

Midpoint of the points=?

Solution:

The midpoint that lies between the two points is given by

(x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})

Where

(x_m, y_m)= coordinates of the midpoint

(x_1, y_1)= coordinates of the first point

(x_2, y_2)= coordinates of the second point

we have,

x_1= 2

y_1= -5

x_2= 4

y_2= -5

Substituting the values in the mid point formula,

(x,y)=(\frac{(2+4)}{2},\frac{(-5-7)}{2})

(x,y)=(\frac{(6)}{2},\frac{(-12)}{2})

(x,y)=(3,-6)

5 0
3 years ago
First, find the area of each rectangle. 3×5 1/6
mote1985 [20]

Answer:

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Step-by-step explanation:

hope this helps!

7 0
3 years ago
What is this rounding to the nearest hundred thousand 289,659
Tema [17]
300,000
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4 0
3 years ago
Read 2 more answers
What would a monthly payment be on a purchase of a $10,000 car at a 5.9% for 4 years?
gizmo_the_mogwai [7]
The current monthly pay can be calculated as follows;
A=p(1/r/100)^n
A=10000
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10000=p(1.005)^48
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the monthly payment will be:
7871/12
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5 0
3 years ago
Read 2 more answers
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