Question

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

• A. (G.M. of middle terms)${}^{no}$ ${}^{of}$ ${}^{terms}$
• B. (A.M. of middle terms)${}^{no}$ ${}^{of}$ ${}^{terms}$
• C. (H.M. of middle terms)${}^{no}$ ${}^{of}$ ${}^{terms}$
• D. (G.M. of middle terms)${}^{no}$ ${}^{of}$ ${}^{terms-1}$

Answer 1

Answer: (A)

(G.M. of middle terms)${}^{no}$ ${}^{of}$ ${}^{terms}$

let the middle terms be $\frac{a}{r}$ and $ar$
so if the number of terms is 2n then the terms are..
$\frac{a}{r^{2n-1}},....,\frac{a}{r},ar,....,a{r}^{2n-1}$
so the product of the 2n terms is $a^{2n}=$ $(a{)}^{2n}$
i.e ${\text{(G.M of middle terms)}}^{no.ofterms}$

Since, $\text{GM of middle terms}=$ $\text{GM of}\left(\frac{a}{d}\right)\text{and}\left(ad\right)=\sqrt{a.a}=a.$