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| 1. |
If p times the pth term of an ap equals to q times the qth term find p+q term |
| Answer» Let the first term and the common difference of the AP be a and d respectively.pth term = a ....... Given{tex} \\Rightarrow {/tex}\xa0a + (p - 1)d = q ....... (1)qth term = p ....... Given{tex} \\Rightarrow {/tex}\xa0a + (q - 1)d = p ....... (2)Subtract\xa0(1) and (2)q - p = (p - 1)d - (q - 1)dq - p = pd - d - qd + dq - p = (p - q)dq - p = -(q - p)dd = -1Substituting d = -1 in equation (1), we geta + (p - 1) (-1) = q{tex} \\Rightarrow {/tex}\xa0a = p + q - 1Now, pth term of the AP= a + (p - 1)d= (p + q - 1) + (p - 1) (-1)= p + q - nHence,(p + q) th\xa0term of the AP= p + q - (p + q)= 0 | |