Mathematics · JEE | SEQUENCES AND SERIES

Consider the following statements about Geometric Progressions: (I) A sequence \( a_1, a_2, a_3, \dots, a_n, \dots \) is a G.P. if each term is non-zero and \( \frac{a_{k+1}}{a_k} = r \) (constant) for \( k \ge 1 \). (II) The \( n^{\text{th}} \) term of a G.P. with first term \( a \) and common ratio \( r \) is \( ar^{n-1} \). (III) The geometric mean of two positive numbers \( a \) and \( b \) is \( \frac{a+b}{2} \). How many of the above statements are correct?

1. A
   Only one
2. B
   Only two
3. C
   Only three
4. D
   None