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

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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