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Question

Find a30a20 for the A.P.
(i) -9,-14,-19,-24,... (ii)a,a+d,a+2d,a+3d,...

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Solution

1-(i) The givien AP is -9,-14,-19,-24,... Clearly the first term a= -9, Common difference d=-5
a30 =a+(n-1)d
=-9+(30-1)(-5)

= 9 + 29 (-5)
=-9-145
= -154
a20 =-9+(20-1)(-5)
=-9+(19)(-5)
=-9-95
= -104
So

a30a20= -154-(-104)
=-154+104
=-50
2 The givien AP is -a,a+d,a+2d,a+3d,...
We know that a30=a+(n-1)d
a30=a+29d
and a20=a+19d
a30a20=a+29d-(a+19d)
+ a+29d -a-19d

=10d


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