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Three numbers are in A.P. Such that their sum is 18 and the sum of their squares is 158. The greatest number among them is:
- a)10
- b)11
- c)12
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Three numbers are in A.P. Such that their sum is 18 and the sum of the...
For an odd number of terms of an AP always take the middle term as a and other terms on either side with a common difference d.
Let the three numbers in A.P. be
(a – d), a & (a + d)
Given (a – d) + a + (a + d) = 18 or 3a = 18
∴ a = 6 …(i)
Further (a – d)2 + a2 + (a + d)2 = 158
⇒ 3a2 + 2d2 = 158
⇒ 2d2 = 158 – 3 × 36
⇒ d2 = 25 or d = ± 5
Then, the numbers are 1, 6, 11.
Thus, the greatest number is 11.
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Three numbers are in A.P. Such that their sum is 18 and the sum of their squares is 158. The greatest number among them is:a)10b)11c)12d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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