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Question
If m th term of an A.P. is n and nth term is m, then write its pth term.
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Solution
Given:
\[a_m = n\]
\[ \Rightarrow a + \left( m - 1 \right)d = n . . . . \left( 1 \right)\]
\[ a_n = m\]
\[ \Rightarrow a + (n - 1)d = m . . . . \left( 2 \right)\]
Solving equations
\[\left( 1 \right) \text { and } \left( 2 \right)\],we get: d = \[- 1\] a = n+m \[- 1\]
p th term:
\[a_p = a + \left( p - 1 \right)d\]
\[ = n + m - 1 + \left( p - 1 \right)\left( - 1 \right)\]
\[ = n + m - p\]
Hence, the pth term is n + m \[-\] p.
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