Question

find the value of p if the numbers x,2x+p,3x+6 are three consecutive terms of ap aloso find the terms

Answer 1

The value of p is 3

So,
$p = 3$


The terms of AP are as follows :-

$x$

$2x + 3$

$3x + 6$





Please refer the above photograph for the used process.


For any value of x, The consecutive terms will be in AP.


For example :-

The AP is x, 2x+3 , 3x+6

So,

If x = 1
The Arithmetic Progression will be :-

$1$
$5$
$9$



If x = 2
The AP will be :-

$2$
$7$
$12$



Similarly the value of x will determine the Arithmetic Progression.




KEY POINTS TO REMEMBER :-


☸️ If a , b and c are the consecutive terms of an AP, They will follow a sequence that :-
$2b = a \: + \: c$



☸️ AP stands for Arithmetic Progression




☸️ D or the common difference remains same between all the adjacent terms of an AP.

In this case,
The common difference is x+3




Thanks!