Insert 4 A.M.s between 4 and 19.

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Solution

Let $A_{1}, A_{2}, A_{3}, A_{4}$ be the 4 A.M.s between 4 and 19.
Then,
$4, A_{1}, A_{2}, A_{3}, A_{4}, 19$ are in A.P. of 6 terms.
$A_{n} = a + (n - 1) d a_{6} = 19 = 4 + (6 - 1) d$
Or d = 3 ...... (i)
Now,
$A_{1} = a + d = 4 + 3 = 7 A_{2} = A_{1} + d = 7 + 3 = 10 A_{3} = A_{2} + d = 10 + 3 = 13 A_{4} = A_{3} + d = 13 + 3 = 16$
The 4 A.M.s between 4 and 19 are 7, 10, 13, 16.

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