Question

Let $T _ { r }$ be the $r ^ { t h }$ term of an A.P. for$r = 1,2,3 , \ldots$. If for some positive integers $m , n$ we have $T _ { m } = \frac { 1 } { n }$ and $T _ { n } = \frac { 1 } { m }$ , then $T _ { m n }$ equals.

• A. $\frac { 1 } { m n }$
• B. $\frac { 1 } { m } + \frac { 1 } { n }$
• C. 1
• D. 0

Answer 1

Answer: (C)

1

Answer 2

$T _ { m } = a + ( m - 1 ) d = \frac { 1 } { n }$ and $T _ { n } = a + ( n - 1 ) d = \frac { 1 } { m }$

On solving $a = \frac { 1 } { m n }$ and $d = \frac { 1 } { m n }$

$\therefore$ $T _ { m n } = a + ( m n - 1 ) d = \frac { 1 } { m n } + ( m n - 1 ) \frac { 1 } { m n } = 1$