Question

For what value of k number 5k,4k -1,and 3k - 2 form an a. P?

Answer 1

Given: 5k, 4k - 1 and 3k - 2.

To find: The value of k so that they form an AP.

Answer:

$\sf Let's\ suppose\ a_1,\ a_2\ and\ a_3\ are\ in\ AP.\\\\\\Then,\\\\\\a_2\ -\ a_1\ =\ a_3\ -\ a_2$

From what we have,

$\sf a_1\ =\ 5k\\\\a_2\ =\ 4k\ -\ 1\\\\a_3\ =\ 3k\ -\ 2$

Using them in the formula we observed,

$\sf 4k\ -\ 1\ -\ 5k\ =\ 3k\ -\ 2\ -\ 4k\ +\ 1\\\\\\-1k\ -\ 1\ =\ -1k\ -\ 1\\\\\\-1\ +\ 1\ =\ -1k\ +\ 1k\\\\\\0\ =\ 0$

Therefore, k can be any value.

Answer 2

Answer:

In an Arithmetic Progression (AP):

The terms have a common difference. Thus:

4k - 1 - 5k = 3k - 2 - (4k - 1)

=> -k + k = 1 - 1

=> k = 0

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