The 4th term of ap is zero prove 25th term of ap is three times it\’s 11th term
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We have,a4\xa0= 0{tex}a + 3d = 0{/tex}{tex}3d = -a{/tex}or {tex}-3d = a{/tex}……….(i)Now,a25\xa0= {tex}a + 24d{/tex}= {tex}-3d + 24d{/tex} [Putting value of a from eq(i)]= {tex}21d{/tex}………..(ii)a11\xa0= {tex}a + 10d{/tex}= {tex}-3d + 10d{/tex}= {tex}7d{/tex}………(iii)From eq(ii) and (iii), we geta25 = 21 da25 = 3(7d)a25\xa0= 3a11Hence Proved