First slide

Arithmetic progression

Question

If m^th term of an A.P. is n and n^th term in m, then its r ^th term is

Moderate

A

$m + n - r$
B

$m + n + r$
C

$m - n + r$
D

$r - (m + n)$

Solution

$\begin{array}{l} a_{m} = n, a_{n} = m \\ \Rightarrow (m - n) d = a_{n} - a_{n} = - (m - n) \\ \Rightarrow d = - 1 \end{array}$
Now, $a_{r} - a_{m} = (r - m) (- 1)$
$\Rightarrow a_{r} = a_{m} - r + m = m + n - r$

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