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प्रश्न
If x + 1, 3x and 4x + 2 are in A.P., find the value of x.
उत्तर
Here, we are given three terms which are in A.P.
First-term `(a_1) = x + 1`
Second term `(a_2) = 3x`
Third term `(a_3) = 4x + 2`
We need to find the value of x. So in an A.P. the difference of two adjacent terms is always constant. So we get
`d = a_2 - a_1`
d = (3x) - (x + 1)
d = 3x - x - 1
d = 2x - 1 .........(1)
Also
`d = a_3 - a_2`
d= (4x + 2) - (3x)
d = 4x - 3x + 2
d = x + 2 ......(2)
Now on equating (1) and (2) we get
2x - 1 = x + 2
2x - x = 2 + 1
x = 3
Therefore for x= 3 these three terms will form an A.P
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