If eleven A.M. s are inserted between 28 and 10, then find the number of integral A.M. s.

Options

A. 5
B. 6
C. 7
D. 8

Answer

A

Explanation

Let 11AM's are `A_(1),A_(2),A_(3),"….."A_(11)`.
Given, `28,A_(1),A_(2),A_(3),"….."A_(11)`,10 are in AP.
`:.d=(10-28)/(12)=-(3)/(2)`
`:.A_(i)=28+id=28-(3)/(2)i`
It is clear that `A_(2),A_(4),A_(6),A_(8),A_(10)` are integral AM's.
Hemce, number of integral AM's are 5.