- Jamie takes out an interest-free loan of \(\pounds 8100\)
Jamie makes a payment every month to pay back the loan.
Jamie repays \(\pounds 400\) in month \(1 , \pounds 390\) in month \(2 , \pounds 380\) in month 3 , and so on, so that the amounts repaid each month form an arithmetic sequence.
- Show that Jamie repays \(\pounds 290\) in month 12
After Jamie's \(N\) th payment, the loan is completely paid back.
- Show that \(N ^ { 2 } - 81 N + 1620 = 0\)
- Hence find the value of \(N\).