Sequence and Series - Geometric Progression

1. Consider the geometric sequence \(-3, 6, -12, 24, \dots\) .[3]
   1. Write down the common ratio.
   2. Find the \(15^{\mathrm{th}}\) term.

Consider the sequence \(x - 3, x + 1, 2x + 8, \dots\) .

2. When \(x = 5\), the sequence is geometric.[2]
   1. Write down the first three terms.
   2. Find the common ratio.
3. Find the other value of \(x\) for which the sequence is geometric.[4]
4. For this value of \(x\), find[3]
   1. the common ratio;
   2. the sum of the infinite sequence.