if x+1 ,3x,4x+2 are in AP the sum of these number
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Answer : 27
Let the first term be a.
Let the common difference be d.
1st term = a...(1)
2nd term = a+d...(2)
3rd term = a+2d...(3)
Adding 1st term and 3rd term we get:
a + (a+2d)
= 2a + 2d
= 2(a+d)
= 2 × 2nd term ( From (2) )
Thus, we can say that :
1st term + 3rd term= 2 × 2nd term
So,
Given AP :
x+1, 3x, 4x+2
Adding this,
x+1 + 4x+2 = 2 × 3x
=> 5x+3 = 6x
» x = 3
So the value of x is 3.
Putting value of x,
x + 1 = 4
3x = 9
4x + 2 = 14
Thus,
Their sum = 4 + 9 + 14 = 27
Answer : 27
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