Question
Find $a_{30} - a_{20}$_ for the A.P.
$a, a + d, a + 2d, a + 3d$, .....
$a, a + d, a + 2d, a + 3d$, .....
✓
Answer
Given,
$a_{30} - a_{20} = a + (30 - 1)d - (a + (20 - 1)d)$($\therefore$ $a_n = a + (n - 1)d)$
$= a + 29d - a - 19d$
$= 10d$
In A.P. $a, a + d, a + 2d, a + 3d$, .....
a is the first term and d is the common difference
$\therefore$ $a_n = a + (n - 1)d$
$\therefore$ $a_{20} = a + (20 - 1)d = a + 19d$
and $a_{30} = a + (30 - 1)d = a + 29d$
$\therefore$ $a_{30} - a_{20} =a + 29d - a - 19d = 10d.$
$a_{30} - a_{20} = a + (30 - 1)d - (a + (20 - 1)d)$($\therefore$ $a_n = a + (n - 1)d)$
$= a + 29d - a - 19d$
$= 10d$
In A.P. $a, a + d, a + 2d, a + 3d$, .....
a is the first term and d is the common difference
$\therefore$ $a_n = a + (n - 1)d$
$\therefore$ $a_{20} = a + (20 - 1)d = a + 19d$
and $a_{30} = a + (30 - 1)d = a + 29d$
$\therefore$ $a_{30} - a_{20} =a + 29d - a - 19d = 10d.$
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