If in an AB ratio of 4th term and 9th term os 1:3 . find the ratio of 12th term and 5th term.
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a4/a9 = 1/3
a4= a+3d
a9=a+8d
a+3d/a+8d = 1/3
3a+9d=a+8d
2a=-1d
-2a=d -(1)
a12=a+11d
a5=a+4d
therefore, a+11d/a+4d
=a+11×-2a/ a+4×-2a. [from (1)]
= a-22a/ a-8a
= -21a/-7a
= 3/1
therefore the ratio is 3:1
a4= a+3d
a9=a+8d
a+3d/a+8d = 1/3
3a+9d=a+8d
2a=-1d
-2a=d -(1)
a12=a+11d
a5=a+4d
therefore, a+11d/a+4d
=a+11×-2a/ a+4×-2a. [from (1)]
= a-22a/ a-8a
= -21a/-7a
= 3/1
therefore the ratio is 3:1
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