Q. 555.0( 1 Vote )

If the first and the nth terms of a G.P are a and b respectively and if p is the product of the first n terms, prove that P2 = (ab)n.

Answer :

Let the G.P be c, cr, cr2, ……….crn

1st term c = a

nth term cr n-1 = b

If n terms is c, cr, cr2, ……….crn-1

Product of n term

p = c.(cr)(cr2)(cr3)……..(crn-1

   = cn.r1+2+………n-1

   = cn 

P2 = (cn)2 2 = c2nrn(n-1) = c2n rn2-n ………….(1)

(ab)n = (c.crn-1)n = (c2rn-1)n = c2n rn2-n ……….(2)

From (1) and (2),

P2 = (ab)n.

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