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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Given the first two terms of H.P is 25and1213
1a=25⇒a=52and,1a+d=1213⇒d=−1712∴an=a+(n−1)d=52+(n−1)−1712=47−17n12⇒1an=1247−17nfor1an(to be largest term,(47−17n)should be smallest positive intergerforn=2,(47−17n)=13forn=1,(47−17n)=30, term can't be taken, since in question it is already be seen that25<1213forn=3,4,...., the term(47−17n) will be negative∴ largest term in the givenH.Pis1213