10th Class Mathematics Solved Paper - Mathematics 2017 Outside Delhi Set-III

  • question_answer For what value of n, are the nth terms of two A.Ps 63, 65, 67,.... and 3, 10, 17,.... equal ?

    Answer:

    \[{{1}^{st}}\]A.P. is 63, 65, 67,...
    \[a=63,\]           \[d=65-63=2\]
                            \[{{a}_{n}}=a+(n-1)d\]
                                \[=63+(n-1)2\]
                                \[=63+2n-2=61+2n\]
    \[{{2}^{nd}}\]A.P. is 3, 10, 17...
    \[a=3,\] \[d=10-3=7\]
                            \[{{a}_{n}}=a+(n-1)d\]
                                \[=3+(n-1)7\]
                                \[=3+7n-7\]
                                \[=7n-4\]
    According to question,
    \[61+2n=7n-4\]
    \[61+4=7n-2n\]
         \[65=5n\]
           \[n=\frac{65}{5}=13\]
           \[n=13\]
    Hence, \[{{13}^{th}}\]term of both A.P. is equal


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