
### Instruction: help me answer this question If the first and the nth term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that P^2 = (ab)^n, think step by step
### Assistant: Since the first term of the G.P. is a, and the last term is b, its product (P) can be expressed as the product of the first term, the common ratio, and the sum of n-1 terms of an arithmetic progression. We then show that P^2 = (ab)^n by using the properties of G.P. and the formula for the sum of an A.P. , The answer is P^2 = (ab)^n
