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,

a_{p} = x.

a_{q} = t

a_{r} = z.

We know that a_{n} = aR^{n-1}

∴ a_{p} = aR^{p-1}= x

a_{q} = aR^{q-1}= y

a_{r} = aR^{r-1}= z

⇒ x^{q-r} = (aR^{p-1})^{q-r}

⇒ y^{r-p} = (aR^{q-1})^{r-p}

⇒ z^{p-q} = (aR^{r-1})^{p-q}

Multiplying the above three equations we get

x^{q-r}.y^{r-p}.z^{p-q} = (a^{q-r}.R^{pq-pr-q+r}). (a^{r-p}.R^{rq-pq-r+p}). (a^{p-q}.R^{pr-qr-p+q})

=(a^{q-r+r-p+p-q}.R^{pq-pr-q+r+rq-pq-r+p+pr-qr-p+q})

= (a^{0}.R^{0})

= 1.

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