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Question

Find a30a20 for the A.P
a,a+d,a+2d,a+3d,........

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Solution

Given A.P is a,a+d,a+2d,a+3d,....
hence the common difference is given by d=an+1an
by putting n=1 in above equation
d=a2a1=(a+d)(d)
d=d
first term of this A.P is
a1=a
the nth term of this A.P is given by
an=a1+(n1)d
an=a+(n1)d.eq(1)


1) For finding the 30th term of sequence (a30) put n=30 in eq(1)
a30=a+(301)d
a30=a+29d

2) For finding the 20th term of sequence (a20)put n=20 in eq(1)
a20=a+(201)
a20=a+19d


now,
a30a20=(a+29d)(a+19d)
a30a20=(29d19d)
a30a2=10d

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