Q. 274.3( 24 Votes )

The 4th term of an AP is zero. Prove that its 25th term is triple its 11th term.

Answer :

Let a be the first term and d be the common difference.

Given: a4 = 0


To prove: a25 = 3 × a11


Now, Consider a4 = 0


a + (4 - 1)d = 0


a + 3d = 0


a = - 3d ………. (1)


Consider a25 = a + (25 - 1)d


a25 = - 3d + 24d (from equation (1))


a25 = 21d ………. (2)


Now, consider a11 = a + (11 - 1)d


a11 = - 3d + 10d (from equation (1))


a11 = 7d ……….(3)


From equation (2) and (3), we get,


a25 = 3 × a11


Hence, proved.


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