# If in an AP, ratio of 4th and 9th term is 1:3, find the ratio of 12th term and 5th term.

2
is it 5th or 15th?

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is it 5th or 15th?

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a+3d/a+8d = 1/3

(a+3d)3 = (a+8d)

3a+9d = a+8d

2a+d = 0

d = -2a

a12/a5

a+11d/a+4d

=a+11*(-2a)/a+4*(-2a)

=a-22a/a-8a

= -21a/-7a

=21/7

=3/1

=3:1

That means, a9 = 3*a4.

Need to find, a12/a5.

a9=a+8d

a4=a+3d

a+8d=3a+9d

d=-2a

a12=a+11d=-21a

a5=a+4d=-7a

So ratio of a12 to a5 = -21a:-7a or 3:1//