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

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