4 The first term of an arithmetic progression is \(a\) and the common difference is - 4 . The first term of a geometric progression is \(5 a\) and the common ratio is \(- \frac { 1 } { 4 }\). The sum to infinity of the geometric progression is equal to the sum of the first eight terms of the arithmetic progression.
- Find the value of \(a\).
The \(k\) th term of the arithmetic progression is zero. - Find the value of \(k\).