Find the 31st term of an ap whose 11th term is 38 &16th term is 73

1.	Find the 31st term of an ap whose 11th term is 38 &16th term is 73
Answer» {tex} a_n=a+(n-1)d{/tex}{tex}a_{11}=a+(11-1)d{/tex}{tex}38=a+10d-------eq(i){/tex}{tex}a_{16}=a+(16-1)d{/tex}{tex}73=a+15d -------eq(ii){/tex}Subtract eq(i) from eq(ii){tex}35=5d{/tex}{tex}d=\\frac{35}{5}=7{/tex}Putt value of d in eq(I){tex}38=a+10×5{/tex}{tex}a=38-50=-12{/tex}Now\xa0{tex}31^{st}{/tex}\xa0term{tex}a_{31}=-12+(31-1)×7=198{/tex}

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