Answer :

Given: 10 × a10 = 15 × a15

To show : a25 = 0


Consider 10 × a10 = 15 × a15


10 [a + (10 - 1)d] = 15 [a + (15 - 1)d]


10a + 90d = 15a + 210d


- 5 a = 120 d


a = - 24d ………………(1)


Now, a25 = a + (25 - 1)d


a25 = a + 24d


a25 = - 24d + 24d (from equation 1)


a25 = 0


Hence, proved.


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