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 four A.M.s between 4 and 19. Then, 4, $A_{1}, A_{2}, A_{3}, A_{4}$ and 19 are in A.P. whose common difference is as follows:
d = $\frac{19 - 4}{4 + 1}$
= 3

$A_{1} = 4 + d = 4 + 3 = 7 A_{2} = 4 + 2 d = 4 + 6 = 10 A_{3} = 4 + 3 d = 4 + 9 = 13 A_{4} = 4 + 4 d = 4 + 12 = 16$
Hence, the required A.M.s are 7, 10, 13, 16.

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