Question

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

Answer 1

Step-by-step explanation:

$\because$ x,(2x+k) and (3x+6) are three consecutive terms of an AP.

$\therefore (2x+k)-x= (3x+6)-(2x+k)\\\\</p><p>\therefore 2x+k-x= 3x+6-2x-k\\\\</p><p>\therefore x+k= x+6-k\\\\</p><p>\therefore k+k= x+6-x\\\\</p><p>\therefore 2k= 6\\\\</p><p>\therefore k= \frac {6}{2} \\\\</p><p>\huge \red {\boxed {\therefore k= 3}}$

Answer 2

Step-by-step explanation:

Step-by-step explanation:

\because∵ x,(2x+k) and (3x+6) are three consecutive terms of an AP.

\begin{gathered} \therefore (2x+k)-x= (3x+6)-(2x+k)\\\\ < /p > < p > \therefore 2x+k-x= 3x+6-2x-k\\\\ < /p > < p > \therefore x+k= x+6-k\\\\ < /p > < p > \therefore k+k= x+6-x\\\\ < /p > < p > \therefore 2k= 6\\\\ < /p > < p > \therefore k= \frac {6}{2} \\\\ < /p > < p > \huge \red {\boxed {\therefore k= 3}} \\\\\end{gathered}

∴(2x+k)−x=(3x+6)−(2x+k)

</p><p>∴2x+k−x=3x+6−2x−k

</p><p>∴x+k=x+6−k

</p><p>∴k+k=x+6−x

</p><p>∴2k=6

</p><p>∴k=

2

6

</p><p>

∴k=3