Question

First term of a G.P. of n terms is a and the last term $l$ The product of all the terms of the G.P. is

• A. $\frac{n}{2}(a+b)$
• B. $(a+b)^{\frac{n}{2}}$
• C. $(al)^{\frac{n}{2}}$
• D. $(al)^n$

Answer 1

Answer: (C)

Product $ = \left(a\right)\left(ar\right) ........\left(ar^{n-1}\right) $
$ = a^{n}r^{1+2+.......+\left(n-1\right)} = a^{n} r^{\frac{n-1}{2}\left(1+n-1\right)} $
$ = a^{n} r^{n\left(\frac{n-1}{2}\right) }$
$= \left(a^{2}r^{n-1}\right)^{n/ 2}$
$= \left(al\right)^{n/ 2}$