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| 1. |
If p times pth term is q times qth term. Show that ( p+q)is term is 0 |
| Answer» p * ap = q * aqp{ a + (p-1) d } = q { a + ( q - 1 ) d }ap + p2d - pd = aq + q2d - qdap - aq = - p2d + q2d - qd + pda (p - q ) = d ( q2 - p2 + p - q )a ( p - q ) = d { ( q - p ) ( q + p) + p - q }a ( p - q ) = d ( p - q ) { -1 ( p + q) + 1 }a = d ( - p - q + 1 ) .... ( 1) ( p + q ) th term = a + (n - 1 ) dhere , n = no. of terms= a + ( p + q - 1 ) d = o .. (2)substituting a = d ( - p - q + 1 ) in ( 2 )= d ( - q - p + 1 ) + ( p + q - 1 ) d= -dp - dq + d + pd + qd - d= 0 | |