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Question

If the first two terms of a H.P. are 2/5 and 12/13 respectively. Then find the largest term ?

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Solution

Given the first two terms of H.P is 25and1213
which means
1a=25a=52and,1a+d=1213d=1712an=a+(n1)d=52+(n1)1712=4717n121an=124717nfor1an(to be largest term, (4717n) should be smallest positive intergerforn=2,(4717n)=13forn=1,(4717n)=30, term can't be taken, since in question it is already be seen that 25<1213forn=3,4,...., the term (4717n) will be negative largest term in the givenH.Pis1213

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