Q. 214.0( 6 Votes )

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

Answer :

Given: a4 = 0


To Prove: a25 = 3 × a11


Now, a4 = 0


a + 3d = 0


a = –3d


We know that,


an = a + (n – 1)d


a11 = –3d + (11 – 1)d [from (i)]


a11 = –3d + 10d


a11 = 7d …(ii)


Now,


a25 = a + (25 – 1)d


a25 = –3d + 24d [from(i)]


a25 = 21d


a25 = 3 × 7d


a25 = 3 × a11 [from(ii)]


Hence Proved


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