Question

One A.P. If the first 4 verses of x, p, y, 2p are, what is the ratio of x and y? answer with explanation.​

Answer 1

Given :-

x , p ,y ,2p are the four tems of an AP.

To find :-

The ratio of x and y

Solution :-

Given that

The four terms of an AP = x , p , y , 2p

Since , they are in A.P.

The common difference is same throughout the A.P.

Common difference (d) = p-x = y-p = 2p-y

On taking p-x = y-p

=> p+p = y+x

=> 2p = y+x

=> x = 2p-y

Therefore, x = 2p-y -------(1)

and

on taking y-p = 2p-y

=>y+y = 2p+p

=> 2y = 3p

=> y = 3p/2

Therefore, y = 3p/2 --------(2)

On substituting the value of y in (1)

x = 2p-(3p/2)

=> x = (4p-3p)/2

=> x = p/2

Therefore, x = p/2 -----------(3)

Now

From (2) & (3)

The ratio of x and y

= x : y

= (p/2) : (3p/2)

= (p/2)/(3p/2)

=> (p/2)/×(2/3p)

=> (p×2)/(2×3p)

=> 2p/6p

=> 1/3

=> 1:3

Therefore, x : y = 1:3

Answer :-

The ratio of x and y is 1:3

Used Concept :-

→ The common difference is same throughout the A.P.

Used formulae:-

→ a : b can be written as a/b

Answer 2

Step-by-step explanation:

Given :-

x , p ,y ,2p are the four tems of an AP.

To find :-

The ratio of x and y

Solution :-

Given that

The four terms of an AP = x , p , y , 2p

Since , they are in A.P.

The common difference is same throughout the A.P.

Common difference (d) = p-x = y-p = 2p-y

On taking p-x = y-p

=> p+p = y+x

=> 2p = y+x

=> x = 2p-y

Therefore, x = 2p-y -------(1)

and

on taking y-p = 2p-y

=>y+y = 2p+p

=> 2y = 3p

=> y = 3p/2

Therefore, y = 3p/2 --------(2)

On substituting the value of y in (1)

x = 2p-(3p/2)

=> x = (4p-3p)/2

=> x = p/2

Therefore, x = p/2 -----------(3)

Now

From (2) & (3)

The ratio of x and y

= x : y

= (p/2) : (3p/2)

= (p/2)/(3p/2)

=> (p/2)/×(2/3p)

=> (p×2)/(2×3p)

=> 2p/6p

=> 1/3

=> 1:3

Therefore, x : y = 1:3

Answer :-

The ratio of x and y is 1:3

Used Concept :-

→ The common difference is same throughout the A.P.

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