Two arithmetic progressions have the same common difference. If the first term of the first progression is 3 and that of the other is 8, then the difference between their $ 3 rd $ term is

Given:

Two arithmetic progressions have the same common difference.

The first term of the first progression is 3 and that of the other is 8.

To do:

We have to find the difference between their \( 3 rd \) terms.

Solution:

Let the first term of the $AP_1$ be $a$ and the common difference be $d$.

Let the first term of the $AP_2$ be $b$ and the common difference be $d$.

According to the question,

$a=3$ and $b=8$

$a_3=a+2d=3+2d$

$b_3=b+2d=8+2d$

Therefore,

$b_3-a_3=(8+2d)-(3+2d)$

$=8-3$

$=5$

 The difference between their third terms is 5.