Question

If 4 times the 4th term of an
a.p. is equal to 9 times the 9th term of the
a.p., what is 13 times the 13th term of this
a.p.?

Answer 1

The nth term of an a.p is a+(n-1)d
The 4th term of an a.p is a+3d
The 9th term of an a.p is a+8d
Given that 4 times the 4th term of an a.p is equal to 9 times the 9th term of an a.p
4(a+3d) = 9 (a+8d)
=> 4a+12d = 9a+72d
=> 4a-9a+12d-72d = 0
=> -5a-60d=0
=> -5(a+12d)=0
=> a+12d=0
The 13th term of an a.p is a+12d.
So, the 13 times of 13th term of the a.p is zero.

Answer 2

Given :

4(a4)= 9 (a9)

nth term of an A.P = an = a+( n-1)d

a4= a+(4-1)d= a+3d

a9= a+(9-1)d= a+8d

A.T.Q

4(a+3d)= 9(a+8d)

4a+12d = 9a+72d

4a-9a= 72d-12d

-5a= 60d

a= - (60/5)d

a= -12d

13(a13) = 13(a+12d)

Put the value of a

13(a13) = 13(-12d+12d)

13(a13) = 13(0)

13(a13) = 0

Hence , the 13 times of 13 term [13(a13)] = 0 (zero )

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Hope this will help you...