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

Question

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

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Answer

Let $A_1, A_2, A_3, A_4$ be the four A.M.s between $4$ and $19.$
Then,
$4, A_1, A_2, A_3, A_4, 19$ are A.P of $6$ terms
$A_n = a + (n - 1)d$
$a_6 = 19 = 4 + (6 - 1)d$
or d = 3 .....(1)
Now,
$A_1 = 4 + d = 4 + 3 = 7$
$A_2 = 4 + 2d = 4 + 6 = 10$
$A_3 = 4 + 3d = 4 + 9 = 13$
$A_4 = 4 + 4d = 4 + 12 = 16$
The $4$ A.M.s between $4$ and $19$ are $7, 10, 13, 16.$

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