0

Guest

Courses New

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

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

Grade:11

1 Answers

Arun
25757 Points
5 years ago
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

Think You Can Provide A Better Answer ?

Other Related Questions on Magical Mathematics[Interesting Approach]

View all Questions »

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More