Question

for what value of k ,are the number of X ,2x + k, 3x + 6 are three consecutive term of AP​

Answer 1

Answer : k = 3

Explanation :

GIVEN :

x , 2x + k and 3x + 6 are the three consecutive terms of an AP.

We know that the difference between the terms is same.

Difference = a2 - a1 = a3 - a2

Then,

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

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

x + k = x + 6 - k

x - x + k + k = 6

2k = 6

k = 6/2

k = 3

Therefore, the value of k is 3.

Answer 2

Answer:

k = 3

Step-by-step explanation:

Given,

x, 2x + k and 3x + 6 are the 3 consecutive terms of an A.P.

Difference between the terms are same.

Difference = a2 - a1 = a3 - a2

Then,

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

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

=> x + k = x + 6 - k

=> x - x + k + k = 6

-x and +x are cancelled.

=> k + k = 6

=> 2k = 6

=> k = 6 / 2

=> k = 3

.°. k = 3