Question

solve as whole not write just answer send through photo it is best ohhh i am fluent in english

Answer 1

Hi there,

nth term of an AP = x+(n-1)y

Given
x+(p-1)y = a   ....(1)
x+(q-1)y = b   ....(2)
x+(r-1)y = c    ....(3)

from above equations

eq(2) - eq(3)
y(q-r) = b-c    ....(4)

eq(3) - eq(1)
y(r-p) = c-a    ....(5)

eq(1) - eq(2)
y(p-q) = a-b   ....(6)

from eq4 and eq5
q-r / b-c = r-p / c-a
(c-a)(q-r) = (b-c)(r-p)
cq - cr - a(q-r) = b(r-p) - cr + cp
cq - cp = a(q-r) + b(r-p)
c(q-p) = a(q-r) + b(r-p)

bringing all terms to same side
a(q-r) + b(r-p) - c(q-p) = 0
a(q-r) + b(r-p) + c(p-q) = 0

Hence proved.

Hope it helped.
Let me know if any doubts.
Cheers !!!