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10th Class Mathematics Arithmetic Progressions Question Bank Arithmetic Progressions

  • question_answer
    In an A.P., the sum of first n terms is \[\frac{3{{n}^{2}}}{2}+\frac{13n}{2}.\]Find its 25th term.             

    A) 80                   

    B)        120     

    C) 60                   

    D)         78      

    Correct Answer: A

    Solution :

    We have given that \[{{S}_{n}}=\frac{3{{n}^{2}}}{2}+\frac{13n}{2}\] 25th term = Sum of 25 terms - Sum of 24 terms             \[={{S}_{25}}-{{S}_{24}}\] Now, \[{{S}_{25}}=1100\] and \[{{S}_{24}}=1020\] \[\therefore \] 25th term\[=1100-1020=80\]


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