Question

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

Answer 1

After inserting eleven A.M.s the new series would have a common diffference $d=\frac{28-10}{11+1}=\frac{3}{2}$

Hence every even A.M. would be integral as it would be of the form

$10+2r\times \frac{3}{2}$ where $r$ is an integer

$=10+3r$

$=13,16,19,22,25$

Hence, $5$ integral A.M.'s.