Q : 15       For what value of \small n, are the \small nth terms of two APs:  \small 63,65,67,... and  \small 3,10,17,... equal?
 

Answers (1)

Given two AP's are
 \small 63,65,67,...   and    \small 3,10,17,...
Let first term and the common difference of two AP's are a , a' and d , d'
a = 63 \ , d = a_2-a_1 = 65-63 = 2
And
a' = 3 \ , d' = a'_2-a'_1 = 10-3 = 7
Now,
Let nth term of  both the AP's are equal
a_n = a'_n
\Rightarrow a+(n-1)d=a'+(n-1)d'
\Rightarrow 63+(n-1)2=3+(n-1)7
\Rightarrow 5n=65
\Rightarrow n=\frac{65}{5} = 13
Therefore, the 13th term of both the AP's are equal

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