If 8th
and 11th term of an A.P. are
in the ratio 3:2, then its 21st
and 5th terms are in the ratio
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a8 = 3
a+7d =3. -1
a11 = 2
a+10d=2 -2
subtracting eq 1 and 2
a+7d =3
a+10d = 2
we get -3d = 1
d=1/-3
put value in eq1
a+7d =3
a+7×1/-3=3
a+7/-3 =3
a + -7/3=3
a= 3+7/3
a= 9+7/3
a = 16/3
a21= a+20d
=16/3+20×1/-3
=16/3 - 20/3
= 16-20/3
= -4/3
a5 =a+4d
= 16/3+4×1/-3
=16/3 -4/3
= 16-4/3
=. 12/3=4
a21 : a5
= -4/3 /4
=-1/3or -1:3
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