In the following APs, find the missing terms in the boxes:
$5, \square, \square, 9\frac{1}{2}$
Given:
Given AP is $5, \square, \square, 9\frac{1}{2}$
To do:
We have to find the missing terms in the box.
Solution:
$a=5$
$a_4=9\frac{1}{2}$
We know that,
$a_{4}=a+(4-1) d$
$5+3 d=\frac{19}{2}$
$3d=\frac{19}{2}-5$
$3d=\frac{19-10}{2}$
$3d=\frac{9}{2}$
$d=\frac{9}{2(3)}$
$d=\frac{3}{2}$
This implies,
$a_{2}=a+(2-1) d$
$=a+d$
$=5+\frac{3}{2}$
$=\frac{13}{2}$
$a_{3}=a_{2}+d$
$=\frac{13}{2}+\frac{3}{2}$
$=\frac{16}{2}$
$=8$
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