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Question
Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.
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Solution
Here, we are given three terms,
First term (a1) = 2x
Second term (a2) = x + 10
Third term (a3) = 3x + 2
We need to find the value of x for which these terms are in A.P. So, in an A.P. the difference of two adjacent terms is always constant. So, we get,
d = a2 - a1
d = (x + 10) - (2x)
d = x + 10 - 2x
d = 10 - x ...............(1)
Also,
d = a3 - a2
d = (3x + 2) - (x + 10)
d = 3x + 2 - x -10
d = 2x - 8 ................(2)
Now, on equating (1) and (2), we get,
10 - x = 2x - 8
2x + x = 10 + 8
3x = 18
x = `18/3`
x = 6
Therefore, for x = 6, these three terms will form an A.P.
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