Question

For what value of k , are the numbers x, 2x + k, and 3x + 6 three consecutive terms of an AP​

Answer 1

Difference=difference

2x+k-x= 3x+6-2x-k

x+k=x+6-k

2k=6

k=3

Answer 2

$\:$

Answer:

We know that for an AP,

Second term-First term= Third term-Second term

=>a2-a1=a3-a2

Now,

Here

a1=x

a2=2x+k

a3=3x+6

If x, 2x+k and 3x+6 are the consecutive terms of an AP, then

2x+k-x=3x+6-(2x+k)

2x-x+k=3x+6-2x-k

x+k=3x-2x+6-k

x+k=x+6-k

Cancelling x from both the sides,

k=6-k

k+k=6

2k= 6

k=6÷2

k=3

Hence,The value of k is 3.