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

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

Question

(A) Let $a$ be the first term and $d$ be the common difference of the $A.P.$The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n-1)d$.Given $a_p =

Vedclass · Accepted Answer

$p+q-r$

Vedclass · Answer

(A) Let $a$ be the first term and $d$ be the common difference of the $A.P.$The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n-1)d$.Given $a_p = q$,we have $a + (p-1)d = q$ $....(1)$Given $a_q = p$,we have $a + (q-1)d = p$ $....(2)$Subtracting equation $(2)$ from equation $(1)$:$(a + (p-1)d) - (a + (q-1)d) = q - p$$(p - 1 - q + 1)d = -(p - q)$$(p - q)d = -(p - q)$$d = -1$Substituting $d = -1$ in equation $(1)$:$a + (p-1)(-1) = q$$a - p + 1 = q$$a = p + q - 1$Now,the $r^{th}$ term is $a_r = a + (r-1)d$.$a_r = (p + q - 1) + (r - 1)(-1)$$a_r = p + q - 1 - r + 1$$a_r = p + q - r$

If the $p^{th}$ term of an $A.P.$ is $q$ and the $q^{th}$ term is $p,$ then its $r^{th}$ term is

Similar Questions

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

The ratio of the $7^{th}$ to the $3^{rd}$ term of an $A.P.$ is $12:5$. Find the ratio of the $13^{th}$ to the $4^{th}$ term.

If $\alpha, \beta$ are the roots of the equation $x^2 - 3x + a = 0$ and $\gamma, \delta$ are the roots of the equation $x^2 - 12x + b = 0$,and $\alpha, \beta, \gamma, \delta$ form an increasing $G.P.$,then $(a, b) = $

If $a^2 + b^2 + 16c^2 = 2(3ab + 6bc + 4ac)$,where $a, b, c$ are non-zero numbers,then $a, b, c$ are in:

If $\log 2, \log (2^{x}-1)$ and $\log (2^{x}+3)$ (all to the base $10$) are three consecutive terms of an Arithmetic Progression,then the value of $x$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module