If p times the {p^{th}} term of an A.P. is eq | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(a) $p\{ a + (p - 1)\,d\} = q\{ a + (q - 1)\,d\} $

$ \Rightarrow $ $a(p - q) + ({p^2} - {q^2})\,d + (q - p)\,d = 0$

$ \Rightarrow $ $(p - q)\{ a

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(a) $p\{ a + (p - 1)\,d\} = q\{ a + (q - 1)\,d\} $

$ \Rightarrow $ $a(p - q) + ({p^2} - {q^2})\,d + (q - p)\,d = 0$

$ \Rightarrow $ $(p - q)\{ a + (p + q - 1)\,d\} = 0$

$ \Rightarrow $ $a + (p + q - 1)\,d = 0$

$ \Rightarrow $${T_{p + q}} = 0$,

$\ \{ \because \;p 
e q\} $ .

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

Similar Questions

If three numbers be in $G.P.$, then their logarithms will be in

When $9^{th}$ term of $A.P$ is divided by its $2^{nd}$ term then quotient is $5$ and when $13^{th}$ term is divided by $6^{th}$ term then quotient is $2$ and Remainder is $5$ then find first term of $A.P.$

The sum of $24$ terms of the following series $\sqrt 2 + \sqrt 8 + \sqrt {18} + \sqrt {32} + .........$ is

The common difference of the $A.P.$ $b_{1}, b_{2}, \ldots,$ $b_{ m }$ is $2$ more than the common difference of $A.P.$ $a _{1}, a _{2}, \ldots, a _{ n } .$ If $a _{40}=-159, a _{100}=-399$ and $b _{100}= a _{70},$ then $b _{1}$ is equal to

Three number are in $A.P.$ such that their sum is $18$ and sum of their squares is $158$. The greatest number among them is