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If eleven A.M. s are inserted between 28...

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

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Assume `A_(1),A_(2),A_(3),…A_(11)` be the eleven A.M.'s between 28 and 10, so 28 `A_(1),A_(2),…A_(11),` 10 are in A.P. Let d be the common difference of the A.P. The number of terms is 13. Now,
`10=T_(13)=T_(1)+12d=28+12d`
or `d=(10-28)/12=-18/12=-3/2`
Therefore, integral A.M.'s are
`28-2(3/2),28-4(3/2),28-6(3/2),`
`28-8(3/2),28-10(3/2)`.
Thus, the number of integral A.M.'s is 5.
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