9 The first term of a geometric progression is 216 and the fourth term is 64.
- Find the sum to infinity of the progression.
The second term of the geometric progression is equal to the second term of an arithmetic progression.
The third term of the geometric progression is equal to the fifth term of the same arithmetic progression. - Find the sum of the first 21 terms of the arithmetic progression.
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The diagram shows the circle \(x ^ { 2 } + y ^ { 2 } = 2\) and the straight line \(y = 2 x - 1\) intersecting at the points \(A\) and \(B\). The point \(D\) on the \(x\)-axis is such that \(A D\) is perpendicular to the \(x\)-axis.