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Question
The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an AP is ______.
Options
6
–6
–2
2
MCQ
Fill in the Blanks
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Solution
The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an AP is 6.
Explanation:
To be in A.P., the middle term must be the average of the first and third terms:
x + 10 = `(2x + (3x + 2))/2`
Simplify RHS:
x + 10 = `(5x + 2)/2`
Cross-multiply:
2(x + 10) = 5x + 2
2x + 20 = 5x + 2
Move terms:
20 − 2 = 5x − 2x
18 = 3x
x = `18/3`
x = 6
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