Question

The pth qth and rth term of an A.P are a,b and c respectively. prove that a (q - r) + b (r - p) + c (p - q)​

Answer 1

Step-by-step explanation:

Let x be the first term and d be the common difference of the given AP. Then,

Tp=x+(p-1)d , Tq=x(q-1)d , Tr=x+(r-1)d.

x+(p-1)d .......(1)

x(q-1)d .......(2)

x(r-1)d .......(3)

On multiplying (1) by (q-r)+b(r-p), (2) by (r-p) and (3) by (p-q) and adding,we get

a(q-r)+b(r-p)+c(p-q)

=x•{(q-r)+(r-p)+(p-q)}+d•{(p-1)(q-r)+(q-1)(r-p)+(r-1)(p-q)}

=(x*0)+(d*0)=0

HENCE PROVED

-KARTIKEYA KESARWANI