If the pth , qth and the rth term of a H.P. be x, y, z respectively, prove that yz(q-r) + zx(r-p) + xy(p-q) = 0.
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Dear student,
given pth term of H.P is x
pth term of A.P is
let first term of A.P=A
common difference=D
..........(1)
similarly, .........(2)
and .............(3)
now (1)-(2), we get
or ..........(4)
similarly,(2)-(3), we get
.........(5)
and (3)-(1),we get
...............(6)
we have to prove,
substituting the values of (p-q),(q-r) and (r-p) from (4),(5) and (6), we get
L.H.S
or
hence proved
Enjoy
given pth term of H.P is x
pth term of A.P is
let first term of A.P=A
common difference=D
..........(1)
similarly, .........(2)
and .............(3)
now (1)-(2), we get
or ..........(4)
similarly,(2)-(3), we get
.........(5)
and (3)-(1),we get
...............(6)
we have to prove,
substituting the values of (p-q),(q-r) and (r-p) from (4),(5) and (6), we get
L.H.S
or
hence proved
Enjoy