If the third term of a GP is 4, then the product of first five terms of the GP is

In a Geometric Progression (GP), let the first term be a and the common ratio be r. The general term is given by T_n = ar^n-1.

According to the question, the third term (T₃) is 4:
T₃ = ar^3-1 = ar² = 4

The product of the first five terms is calculated as:
Product = T₁ × T₂ × T₃ × T₄ × T₅
Product = a × (ar) × (ar²) × (ar³) × (ar⁴)
Product = a^(1+1+1+1+1) × r^(0+1+2+3+4)
Product = a⁵r¹⁰

This expression can be rewritten as:
Product = (ar²)⁵

Substituting the value of ar² = 4 from the given information:
Product = 4⁵

Thus, the product of the first five terms is 4⁵, which corresponds to option C.