Question

Find $a_{30}-a_{20}$ for the A.P.
(i) -9,-14,-19,-24,... (ii)a,a+d,a+2d,a+3d,...

Answer 1

1-(i) The givien AP is -9,-14,-19,-24,... Clearly the first term a= -9, Common difference d=-5
$a_{30}$ =a+(n-1)d
=-9+(30-1)(-5)

= 9 + 29 (-5)
=-9-145
= -154
$a_{20}$ =-9+(20-1)(-5)
=-9+(19)(-5)
=-9-95
= -104
So

$a_{30}$−$a_{20}$= -154-(-104)
=-154+104
=-50
2 The givien AP is -a,a+d,a+2d,a+3d,...
We know that $a_{30}$=a+(n-1)d
$a_{30}$=a+29d
and $a_{20}$=a+19d
$a_{30}$−$a_{20}$=a+29d-(a+19d)
+ a+29d -a-19d

=10d