In an mathrm{A.P.} if m^{text {th }} term is n and n^{text {th }} term is m, where m ≠ n , {p^{th}

English

Gujarati

Hindi

8. Sequences and Series

medium

In an $\mathrm{A.P.}$ if $m^{\text {th }}$ term is $n$ and the $n^{\text {th }}$ term is $m,$ where $m \neq n$, find the ${p^{th}}$ term.

A

$n+m-p$

B

$n+m-p$

C

$n+m-p$

D

$n+m-p$

Solution

We have $a_{m}=a+(m-1) d=n,$ ……$(1)$

and $\quad a_{n}=a+(n-1) d=m$ ………$(2)$

Solving $(1)$ and $(2),$ we get

$(m-n) d=n-m,$ or $d=-1,$ ………..$(3)$

and $\quad a=n+m-1$ ………..$(4)$

Therefore $\quad a_{p}=a+(p-1) d$

$=n+m-1+(p-1)(-1)=n+m-p$

Hence, the $p^{\text {th }}$ term is $n+m-p$

Standard 11

Mathematics

Share

Similar Questions

The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$ , then what is the length of its smallest side ?

medium

(IIT-2017)

If the sum of first $n$ terms of an $A.P.$ is $c n^2$, then the sum of squares of these $n$ terms is

hard

(IIT-2009)

Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=n \frac{n^{2}+5}{4}$

medium

Let $x_n, y_n, z_n, w_n$ denotes $n^{th}$ terms of four different arithmatic progressions with positive terms. If $x_4 + y_4 + z_4 + w_4 = 8$ and $x_{10} + y_{10} + z_{10} + w_{10} = 20,$ then maximum value of $x_{20}.y_{20}.z_{20}.w_{20}$ is-

normal

If the angles of a quadrilateral are in $A.P.$ whose common difference is ${10^o}$, then the angles of the quadrilateral are

medium