Find the first six terms of the recursive sequence.

{eq}a_{1} = 1 + a_n + 1 = \sqrt3a_n {/eq}

Question:

Geometric Sequence:

This problem involves finding the terms of a geometric sequence. A geometric sequence is a sequence of numbers where each pair of consecutive terms have a common ratio. For example, if the geometric sequence starts with {eq}\displaystyle a {/eq} and has a common ratio of {eq}\displaystyle r {/eq}, then we can express the sequence as,

{eq}\displaystyle S = a, ar ,ar^2 , \cdot \cdot \cdot {/eq}

Thus any {eq}\displaystyle n^{th} {/eq} term of the sequence can be expressed as {eq}\displaystyle T_n =a r^{n-1} {/eq}

Answer and Explanation: 1