If the {p^{th}},;{q^{th}} and {r^{th}} term o | vedclass

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

Question

(c) Suppose that first term and common difference of $A.P.$'s are $A$ and $D$ respectively.

Now, ${p^{th}}$ term $ = A + (p - 1)D = a$ &hellip;

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(c) Suppose that first term and common difference of $A.P.$'s are $A$ and $D$ respectively.

Now, ${p^{th}}$ term $ = A + (p - 1)D = a$ &hellip;..$(i)$

${q^{th}}$term $ = A + (q - 1)D = b$ ......$(ii)$

and ${r^{th}}$ term $ = A + (r - 1)D = c$ &hellip;..$(iii)$

So, $a(q - r) + b(r - p) + c(p - q)$

$ = a\left\{ {\frac{{b - c}}{D}} \right\} + b\left\{ {\frac{{c - a}}{D}} \right\} + c\left\{ {\frac{{a - b}}{D}} \right\}$

$ = \frac{1}{D}(ab - ac + bc - ab + ca - bc) = 0$.

If the ${p^{th}},\;{q^{th}}$ and ${r^{th}}$ term of an arithmetic sequence are $a , b$ and $c$ respectively, then the value of $[a(q - r)$ + $b(r - p)$ $ + c(p - q)] = $

Similar Questions

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

In an $A.P.,$ the first term is $2$ and the sum of the first five terms is one-fourth of the next five terms. Show that $20^{th}$ term is $-112$

If ${\log _5}2,\,{\log _5}({2^x} - 3)$ and ${\log _5}(\frac{{17}}{2} + {2^{x - 1}})$ are in $A.P.$ then the value of $x$ is :-

Let $3,7,11,15, \ldots, 403$ and $2,5,8,11, \ldots, 404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to.....................

Find the sum to $n$ terms of the $A.P.,$ whose $k^{\text {th }}$ term is $5 k+1$