Question

if 9 times the 9th term of an A.P. is equal to 13 times its 13th term, show that the 22nd term of an A.P. is zero



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Answer 1

Given that 9 times, the 9th term of an AP is = 13 times its 13th term.

= > 9 * a9 = 13 * a13

= > 9(a + 8d) = 13(a + 12d)

= > 9a + 72d = 13a + 156d

= > 13a + 156d - 9a - 72d = 0

= > 4a + 84d = 0

= > 4a = -84d

= > a = -21d  ----- (1)


Now,

22th term = a + 21d

                  = -21d + 21d

                  = 0.



Therefore 22nd term is equal to 0.


Hope this helps!

Answer 2

Hi,

Please see the attached file!



Thanks