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Question
Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.
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Solution
For the first series, a = 3,
\[d_1\] = 7
For the second series, b = 63,
\[d_2\] = 2
Given:
\[a_n = b_n \]
\[ \Rightarrow a + \left( n - 1 \right) d_1 = b + \left( n - 1 \right) d_2 \]
\[ \Rightarrow 3 + \left( n - 1 \right)7 = 63 + \left( n - 1 \right)2\]
\[ \Rightarrow 3 + 7n - 7 = 63 + 2n - 2\]
\[ \Rightarrow 5n = 65\]
\[ \Rightarrow n = 13\]
Hence, the 13th terms of both the series are the same.
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