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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.
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