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 If a1, a2, a3 represents first, second and third terms of an AP respectively, the first terms is 2 and (a1 + a2)a3 is minimum, then the common difference is equal to
  • a)
    5/2
  • b)
    -5/2
  • c)
    2/5
  • d)
    -2/5
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If a1, a2, a3represents first, second and third terms of an AP respect...
Given:
a1 = 2
(a1 + a2)a3 is minimum

To find:
Common difference

Solution:
Let d be the common difference of the AP.

Then,
a2 = a1 + d = 2 + d
a3 = a2 + d = 2 + d + d = 2 + 2d

(a1 + a2)a3 = (2 + 2d)(2 + 2d) = 4 + 8d + 4d^2

To find the minimum value of (a1 + a2)a3, we need to differentiate it with respect to d and equate it to zero.

d/dx [(a1 + a2)a3] = 8 + 8d = 0
=> d = -1

Therefore, the common difference of the AP is -1, i.e. d = -1.

Hence, the correct option is (b) -5/2.
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If a1, a2, a3represents first, second and third terms of an AP respectively, the first terms is 2 and (a1+ a2)a3is minimum, then the common difference is equal toa)5/2b)-5/2c)2/5d)-2/5Correct answer is option 'B'. Can you explain this answer?
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