Question

Verify each of the following is an A.P or not?

(i) x+y, (x+1)+y, (x+1)+(y+1),- - -

(ii) x, 2x+1, 3x+2, 4x+3, - - - (iii) x, 2x, 3x, 4x, - - -​

Answer 1

Answer:

(i)x+1+y-x-y=1,x+1+y+1-x-1-y=1

since,it is an AP

(ii)it is an AP

(iii)it is an AP

Answer 2

1 . x + y , (x+1) + y , ( x+1 ) + (y +1)

Find the Arithmetic mean

===>( x + y + x+1 + y + 1) / 2 = 2(x+y) + 2 / y

= x+ y + 1

= (x + 1) + y

it is the middle term

So it is an A P

2. x , 2x +1 , 3x +2

find the Arithmetic mean

====> ( x + 3x + 2) / 2 = (4x + 2) / 2

= 2x+1

it is the middle term

So it is an AP

3. x , 2x , 3x

Arithmetic mean

===> (x+ 3x) / 2 = 4x /2

= 2x

2x is the middle term

So it is an AP