7. Each year, Abbie pays into a savings scheme. In the first year she pays in \(\pounds 500\). Her payments then increase by \(\pounds 200\) each year so that she pays \(\pounds 700\) in the second year, \(\pounds 900\) in the third year and so on.
- Find out how much Abbie pays into the savings scheme in the tenth year.
Abbie pays into the scheme for \(n\) years until she has paid in a total of \(\pounds 67200\).
- Show that \(n ^ { 2 } + 4 n - 24 \times 28 = 0\)
- Hence find the number of years that Abbie pays into the savings scheme.