Q. 55.0( 2 Votes )

If and terms of a G.P. are x, y, z respectively, then write the value of .

Answer :

Let the first term be a and the common ratio be R.

According to the question,

ap = x.

aq = t

ar = z.

We know that an = aRn-1

ap = aRp-1= x

aq = aRq-1= y

ar = aRr-1= z

xq-r = (aRp-1)q-r

yr-p = (aRq-1)r-p

zp-q = (aRr-1)p-q

Multiplying the above three equations we get

xq-r.yr-p.zp-q = (aq-r.Rpq-pr-q+r). (ar-p.Rrq-pq-r+p). (ap-q.Rpr-qr-p+q)


= (a0.R0)

= 1.

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