A.p.

[Abdul Quadeer]

1. The problem statement, all variables and given/known data

Let An be the nth term of an A.P. and if A7 = 15, then the value of the c.d. that would make A3 x A7 x A12 greatest is :

1)9
2)9/4
3)3/8
4)18

2. Relevant equations



3. The attempt at a solution

Applying AM>=GM

A3+A7+A12/3 >= (A3 x A7 x A12)^1/3

given that A+6d=15
therefore 3A+19d=45

The previous expression reduces to 45+d/3 >= (A3 x A7 x A12)^1/3
cubing the inequality.
(45+d/3)^3 >= (A3 x A7 x A12)

From the choices, 18 will make RHS greatest. But that is not correct!
Any help appreciated.

[The legend]

nice one.. it is.. sure some iit problem
I believe your 2nd last statement is wrong because 18 makes the LHS greatest not RHS and RHS has to be lesser than LHS.

Actually i tried a different approach and i'll give you a hint.
Use the maxima and minima properties and differentiate finding out the values of d. (you will get 2 values ..though one will be eliminated)

[Abdul Quadeer]

Yes, 18 makes the LHS greatest. Since RHS is </= LHS, greater LHS implies greater RHS.
Any way I got the answer by your method :smile:
I just wanted to know what was wrong in this.

[The legend]

Your method doesnt exactly give you the answer.... it just tells you when LHS is greatest and gives no info about RHS(which is what you want). Though this approach may be modified to get the answer.
(I will try that out)