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The 6th term of an AP is equal to 2, the...

The `6th` term of an `AP` is equal to `2`, the value of the common difference of the `AP` which makes the product `a_1a_4a_5` least is given by

A

`8/5`

B

`4/5`

C

`2/3`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`a + 5d =2, P = a_(1) a _(4) a_(5)`
` =a ( a_3d) (a + 4d)`
` = (2-5d) (2-2d) (2-d)`
` P= 2 (4- 16d + 17d ^(2)-5d ^(3))`
`P =2 (-16+ 34d -15d ^(2)) =0`
`d =2/3 and 8/5`
For least product `d =2//3`
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