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

 ${{1}^{st}}$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