The 2nd, 3rd and 4th term of an ap are x-2,5,x+2 respectively ,calculate the value of x
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To find the value of x in the given arithmetic progression (AP), we can use the formula for the nth term of an AP.
The formula for the nth term of an AP is:
An = A + (n-1)d
where:
An is the nth term,
A is the first term,
n is the number of terms, and
d is the common difference between consecutive terms.
In this case, we are given the 2nd, 3rd, and 4th terms of the AP:
2nd term = x - 2
3rd term = 5
4th term = x + 2
Since the 3rd term is given as 5, we can substitute this into the formula:
5 = A + (3-1)d
To find the common difference (d), we subtract the 2nd term from the 3rd term:
5 - (x - 2) = 5 - x + 2 = 7 - x
Now, we can rewrite the formula using the 4th term:
x + 2 = A + (4-1)d
Since the common difference is the same, we can equate the two formulas:
7 - x = x + 2
Solving this equation, we can simplify it to:
2x = 5
Finally, we divide both sides of the equation by 2:
x = 5/2
Therefore, the value of x is 5/2.