Q5 of 24 Page 115

If 10 times the 10th term of an A.P is equal to 15 times the 15th term. Show that 25th term of an A.P is zero.

Let the first term of AP be ‘a’ and common difference be ‘d’.


We know, nth term of an AP is


an = a + (n – 1)d


Given, that


10a10 = 15a15


⇒ 10(a + 9d) = 15(a + 14d)


⇒ 10a + 90d = 15a + 210d


⇒ 5a + 120d = 0


⇒ a + 24d = 0


⇒ a + (25 – 1)d = 0


⇒ a25 = 0


Hence, Proved!


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