In the following APs, find the missing terms in the boxes:
$\square, 13, \square, 3$

Given:

Given AP is $\square, 13, \square, 3$

To do:

We have to find the missing term in the box.

Solution:

$a=13$

We know that,

$a_{2}=a+(2-1) d$

$a+d=13$......(i)

$a_{4}=3$

$a_{4}=a+(4-1) d$

$a+3 d=3$.........(ii)

Subtracting (i) from (ii), we get, 

$a+3d-a-d=3-13$

$2d=-10$

$d=\frac{-10}{2}$

$d=-5$

This implies,

$a+d =13$

$a+(-5)=13$

$a=13+5$

$a=18$

$a_{3}=a+2 d$

$=18+2(-5)$

$=18-10$

$=8$

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Updated on: 10-Oct-2022

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