The third term of a GP is 4; Find the product of its five terms.

Given that the third term of the GP, a3 = 4

Let us assume the GP mentioned in the question be

$\frac{\mathrm{A}}{\mathrm{R}^{2}}, \frac{\mathrm{A}}{\mathrm{R}}, \mathrm{A}, \mathrm{AR}, \mathrm{AR}^{2}$

With the first term $\frac{\mathrm{A}}{\mathrm{R}^{2}}$ and common ratio $\mathrm{R}$.

Now, the third term in the assumed GP is A.

So, A = 4 (given data)

Now

Product of the first five terms of $G P=\frac{A}{R^{2}} \times \frac{A}{R} \times A \times A R \times A R^{2}=A^{5}$

So, the required product $=A^{5}=4^{5}=1024$

∴ The product of first five terms of a GP with its third term 4 is 1024.