23. (a) For process to identify the common ratio - Edexcel - GCSE Maths - Question 23 - 2022 - Paper 1

To find the ratio of the 8th and 6th terms in a geometric sequence, we can use the general formula for the nth term, which is given by:

$a_n = a_1 \cdot r^{n-1}$

Thus, the ratio of the 8th ($a_8$) and 6th ($a_6$) terms can be calculated as:

$\frac{a_8}{a_6} = \frac{\sqrt{5}/2}{\sqrt{3}} = \frac{\sqrt{5}}{\sqrt{9}} = \sqrt{\frac{5}{9}}$

To determine the 2nd term of the sequence, the value can be derived from the general term formula utilized earlier:

$a_2 = a_1 \cdot r^{2-1} = a_1 \cdot r = \frac{\sqrt{5}}{2}$

To find the first term of the sequence, backtrack from the known terms and use the common ratio. Assuming the common ratio is known, the formula used can be:

$x_1 = \frac{\sqrt{2}}{2}$

This establishes the first term in relation to the geometric progression.