A) n = 6
B) n = 12
C) n = 13
D) n = 16
Correct Answer: C
Solution :
(c): If nth terms of the AP?s 63, 65, 67,?..and 3, 10, 17,?.. are equal. Here, first term of first AP = 63 Common difference of first AP \[\left( {{d}_{1}} \right)=65-63=2\] and first term of second AP \[\left( {{d}_{1}} \right)=3\] Common difference of second AP \[\left( {{d}_{2}} \right)=10-3=7\] Then by condition nth term of both AP?s are equal. \[\therefore \,\,\,63+(n-1)2=3+(n-1)7\] \[\Rightarrow \,\,7(n-1)-2(n-1)=63-3\] \[[\because {{a}_{n}}=a+(n-1)d]\] \[\Rightarrow (n-1)(7-2)=60\] \[\Rightarrow 5(n-1)=60\] \[\Rightarrow (n-1)=\frac{60}{5}=12\] \[\Rightarrow n=12+1=13\] Hence, the 13th terms of the two given Aps are the same.
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