- #1

zorro

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## Homework Statement

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

## Homework Equations

## 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.