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Grade: 11

                        

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

3 years ago

Answers : (1)

Arun
24742 Points
							
a + 5d = 2
d >1
Now
a1* 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 this
Hence on solving
f'(d) = - (15 d² - 34d +16)
 
Similarly
f''(d) = -(30 d -34)
f(d) is maximum when f'(d) = 0 & f''(d)
On solving
d = 2/3,  8/5
For d = 8/5,  f"(d) = -14
Hence d = 8/5 is the answer
3 years ago
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