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the 6th term of an AP is 2 and its common difference is greater than 1. The value of the common difference of the progression so that the product of the 1st,4th and 5th terms is greatest is

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3 years ago

Arun
24742 Points
```							a + 5d = 2d >1Nowa1* a4* a5 = (a)(a+ 3d)(a+ 4d) = (2 -5d)(2 -2d)(2 -d)= 2(2- 5d)(1- d)(2 - d) = f(d)We have to maximize thisHence on solvingf'(d) = - (15 d² - 34d +16) Similarlyf''(d) = -(30 d -34)f(d) is maximum when f'(d) = 0 & f''(d) On solvingd = 2/3,  8/5For d = 8/5,  f"(d) = -14 Hence d = 8/5 is the answer
```
3 years ago
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### Course Features

• 731 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions