Question

If a G.P. having $2n+1$ terms whose most middle terms is m, then product of its first $2n+1$ terms is

• A. $m^{2n+1}$
• B. $n^{2n+1}$
• C. $.n^{2m}$
• D. $m^{2x}$

Answer 1

Answer: (A)

$m^{2n+1}$

Let the first 2n+1 terms are
$a_1,a_2,a_3....a_n,a_{n+1},a_{n+2},...a_{2n+1}$
Fact $a_1{a}_{2n+1}=a_2{a}_{2n}=....=a_n{a}_{n+2}=(a_{n+1}{)}^2=m^2$
Now
$a_1,a_2,a_3...a_{2n+1}=\left(a_1{a}_{2n+1}\right)\left(a_2{a}_{2n}\right)....\left(a_n{a}_{n+2}\right)\left(a_{n+1}\right)=(m^2{m}^2{m}^2.....m^2)\cdot m=m^{2n+1}$