(i) The sum of the first 3 terms of a geometric progression is given by:

\(a + ar + ar^2 = 35\)

Substitute \(r = -\frac{2}{3}\):

\(a + a(-\frac{2}{3}) + a(-\frac{2}{3})^2 = 35\)

\(a - \frac{2}{3}a + \frac{4}{9}a = 35\)

Combine terms:

\(a(1 - \frac{2}{3} + \frac{4}{9}) = 35\)

\(a(\frac{9}{9} - \frac{6}{9} + \frac{4}{9}) = 35\)

\(a(\frac{7}{9}) = 35\)

\(a = 35 \times \frac{9}{7}\)

\(a = 45\)

(ii) The sum to infinity of a geometric progression is given by:

\(S_\infty = \frac{a}{1-r}\)

Substitute \(a = 45\) and \(r = -\frac{2}{3}\):

\(S_\infty = \frac{45}{1 - (-\frac{2}{3})}\)

\(S_\infty = \frac{45}{1 + \frac{2}{3}}\)

\(S_\infty = \frac{45}{\frac{5}{3}}\)

\(S_\infty = 45 \times \frac{3}{5}\)

\(S_\infty = 27\)