Q. 224.8( 11 Votes )

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

Answer :

Given: 10 × a10 = 15 × a15


To Prove: a25 = 0


Now,


10 × (a + 9d) = 15 × (a + 14d)


10a + 90d = 15a + 210d


10a – 15a = 210d – 90d


–5a = 120d


a = –24d …(i)


Now,


an = a + (n – 1)d


a25 = –24d + (25 – 1)d [from (i)]


a25 = –24d + 24d


a25 = 0


Hence Proved


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