Question

If the number of terms in a G.P. is odd, then product of terms$=$

• A. (middle term)${}^{no}$ ${}^{of}$ ${}^{terms}$
• B. (middle term)${}^{no}$ ${}^{of}$ ${}^{terms-1}$
• C. (middle term)${}^{no}$ ${}^{of}$ ${}^{terms+2}$
• D. (middle term)${}^{no}$ ${}^{of}$ ${}^{terms+1}$

Answer 1

The correct option is A (middle term)${}^{no}$ ${}^{of}$ ${}^{terms}$

let the middle term be $a_0$
so if the number of terms is $2n+1$ then the terms are
$\frac{a_0}{r^n}\frac{a_0}{r^{n-1}}.....a_0.....a_0{r}^{n-1}{a}_0{r}^n$
so the product of the $2n+1$ terms is simply $a_0^{2n+1}$
i.e $(middleterm{)}^{no.ofterms}$