Question

If $p$ times the $p ^ { t h }$ term of an A.P. is equal to $q$ times the $q ^ { t h }$ term of an A.P., then $( p + q ) ^ { t h }$ term is.

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (A)

0

Answer 2

$p \{ a + ( p - 1 ) d \} = q \{ a + ( q - 1 ) d \}$

$\Rightarrow$ $a ( p - q ) + \left( p ^ { 2 } - q ^ { 2 } \right) d + ( q - p ) d = 0$

$\Rightarrow$ $( p - q ) \{ a + ( p + q - 1 ) d \} = 0$

$\Rightarrow$ $a + ( p + q - 1 ) d = 0$ $\Rightarrow$ $T _ { p + q } = 0$ , $\{ \because p \neq q \}$.