if x+2 ,2x, x+3 are three consecutive terms of AP then find x
can I get fast and correct ans please ​

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1. [tex]{Solution}[/tex]

   Given :-

   x +2 , 2x , x+3 are in A.P

   To find :-

   Value of x

   SOLUTION:-

   As they are in A.P Since, their terms difference should be same

   If a, b , c are in A.P

   c – b = b – a So,

   x + 2 , 2x , x+3

   • a= x+2
   • b = 2x
   • c = x+3

   c – b = b- a

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

   x+3 -2x = 2x -x -2

   x-2x + 3 = x-2

   -x + 3 = x-2

   -x -x = -3 -2

   -2x = -5

   2x = 5

   x = 5/2

   So, the value of x is 5/2

   Know more:-

   A.P means Arthemetic progression That means it follows a certain pattern that is The given sequence common difference should be same

   Examples :-

   2, 4 , 6 , 8 , 10. . . .

   It is a Arthemetic progression beacuse its common difference is same i.e

   10- 8 = 2

   8 – 6 = 2

   6 – 4 = 2

   4 – 2 = 2

   If you observe the difference that is 2 ,Since it is in A.P .

   2, 4 , 6 , 8 , 10 .. . In this progression,

   a = 2 [first term]

   d = 2[common difference]

   n = nth term

   For finding nth term we have formula

   an = a+(n-1) d

   For finding sum of the terms we have formula that is

   Sn = n/2 × 2a+(n-1)d

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